2024-11-01 | | Total: 37

We study a conformal field theory that arises in the infinite-volume limit of a spin chain with $U_q(sl_2)$ global symmetry. Most operators in the theory are defect-ending operators which allows $U_q(sl_2)$ symmetry transformations to act on them in a consistent way. We use Coulomb gas techniques to construct correlation functions and compute all OPE coefficients of the model, as well as to prove that the properties imposed by the quantum group symmetry are indeed satisfied by the correlation functions. In particular, we treat the non-chiral operators present in the theory. Free boson realization elucidates the origin of the defects attached to the operators. We also comment on the role of quantum group in generalized minimal models.

We study quantum field theories which have quantum groups as global internal symmetries. We show that in such theories operators are generically non-local, and should be thought as living at the ends of topological lines. We describe the general constraints of the quantum group symmetry, given by Ward identities, that correlation functions of the theory should satisfy. We also show that generators of the symmetry can be represented by topological lines with some novel properties. We then discuss a particular example of $U_q(sl_2)$ symmetric CFT, which we solve using the bootstrap techniques and relying on the symmetry. We finally show strong evidence that for a special value of $q$ a subsector of this theory reproduces the fermionic formulation of the Ising model. This suggests that a quantum group can act on local operators as well, however, it generically transforms them into non-local ones.

Using a renormalization-inspired perturbation expansion we show that oscillons in a generic field theory in (1+1)-dimensions arise as dressed Q-balls of a universal (up to the leading nonlinear order) complex field theory. This theory reveals a close similarity to the integrable complex sine-Gordon model which possesses exact multi-$Q$-balls. We show that excited oscillons, with characteristic modulations of their amplitude, are two-oscillons bound states generated from a two $Q$-ball solution.

In this paper, we study a free scalar field in a specific (1+1)-dimensional curved spacetime. By introducing an algebraic state that is locally Hadamard, we derive the renormalized Wightman function and explicitly calculate the covariantly conserved quantum energy-momentum tensor up to a relevant order. From this result, we show that the Hadamard renormalization scheme, which has been effective in traditional quantum field theory in curved spacetime, is also applicable in the quantum inhomogeneous field theory. As applications of this framework, we show the existence of an Unruh-like effect for an observer slightly out of the right asymptotic region, as well as a quantum frictional effect on the bubble wall expansion during the electroweak phase transition in the early universe. Consequently, this study validates the consistency of our method for constructing meaningful physical quantities in quantum inhomogeneous field theory.

In this paper, we investigate the Hilbert space factorisation problem of two-sided black holes in high dimensions. We demonstrate that the Hilbert space of two-sided black holes can be factorized into the tensor product of two one-sided bulk Hilbert spaces when the effect of non-perturbative replica wormholes is taken into account. We further interpret the one-sided bulk Hilbert space as the Hilbert space of a one-sided black hole. Therefore, since the Hilbert space of a two-sided black hole can be obtained from the tensor product of two single-sided black hole Hilbert spaces, we consider this as an embodiment of the ER=EPR conjecture, and we show when the entanglement between the two single-sided black holes is sufficiently strong, the (Lorentzian) geometry of a two-sided black hole will emerge.

We conduct a mode analysis of a general U(1)-charged first-order relativistic hydrodynamics within the framework of the effective field theory of dissipative fluids in a Minkowski background. The most general quadratic action for collective excitations around hydrodynamic solutions -- specifically, the Nambu-Goldstone (NG) modes associated with the symmetry-breaking pattern induced by external fields -- is derived. It is found that the hydrodynamical frame invariants write the first-order dispersion relations in the low energy limit. In thermodynamical viscous fluids realized by integrating out fast modes, unitarity and local KMS symmetry for its underlying UV theory are guaranteed. Then, we find that first-order hydrodynamics are stable if the null energy condition is satisfied. As the NG modes nonlinearly realize the diffeomorphism symmetries, our mode analysis is valid in any coordinate systems, including Lorentz-transformed references. We also comment on the causal structure for the diffusive modes based on the retarded Green functions for the stochastic NG mode.

Physical theories have a limited regime of validity and hence must be accompanied by a breakdown diagnostic to establish when they cease to be valid as parameters are varied. For perturbative theories, estimates of the first neglected order offer valuable guidance, but one is often interested in sharp bounds beyond which perturbation theory necessarily fails. In particle physics, it is common to employ the bounds on partial waves imposed by unitarity as such a diagnostic. Unfortunately, these bounds don't extend to curved spacetime, where scattering experiments are challenging to define. Here, we propose to use the growth of entanglement in momentum space as a breakdown diagnostic for perturbation theory in general field theories. This diagnostic can be readily used in cosmological spacetimes and does not require any flat spacetime limit. More in detail, we consider the so-called purity of the reduced density operator constructed by tracing out all but one of the Fourier modes in an effective theory and we present a diagrammatic technique to compute it perturbatively. Constraints on the theory's regime of validity are then derived when the perturbative purity violates its unitarity bounds. In flat spacetime, we compare these purity bounds to those from partial waves. We find general qualitative agreement but with remarkable differences: purity bounds can be sometimes weaker, but other times they exist when no partial wave bounds exist. We then derive purity bounds for scalar field theories in de Sitter spacetime for a variety of interactions that appear in inflationary models. Importantly, our bounds make no reference to time evolution and in de Sitter they depend exclusively on scale-invariant ratios of the physical kinematics.

In this paper, we consider a Carroll magnetic limit of a one-loop scalar effective action. We work on general static backgrounds and compute both divergent and finite parts of the effective action in this limit. We show, that the divergent part can be removed by adding local counterterms. The finite part is related to an effective action in a lower dimensional theory which however does not coincide in general with the one obtained by a Carroll limit in the classical counterpart.

Using the Chern-Simons formulation of AdS3 gravity as well as the Costello-Witten-Yamazaki (CWY) theory for quantum integrability, we construct a novel topological 4D gravity given by Eq(5.1) with observables based on gravitational gauge field holonomies. The field action $S^{grav}_{4D}$ of this gravity has a gauge symmetry $SL(2,\mathbb{C})$ and reads also as the difference $S^{CWY_{L}}_{4D}-S^{CWY_{R}}_{4D}$ with 4D Chern-Simons field actions $S^{CWY_{L/R}}_{4D}$ given by left/right CWY theory Eq(3.9). We also use this 4D gravity derivation to build observables describing gravitational topological defects and their interactions. We conclude our study with few comments regarding quantum integrability and the extension of AdS$_{3}$/CFT$_{2}$ correspondence with regard to the obtained topological 4D gravity.

We discuss the transition between black strings and fundamental strings in the presence of a compact dimension, $\mathbb{S}^1_z$. In particular, we study the Horowitz-Polchinski effective field theory in $\mathbb{R}^d\times\mathbb{S}^1_z$, with a reduction on the Euclidean time circle $\mathbb{S}_\tau^1$. The classical solution of this theory describes a bound state of self-gravitating strings, known as a ``string star'', in Lorentzian spacetime. By analyzing non-uniform perturbations to the uniform solution, we identify the critical mass at which the string star becomes unstable towards non-uniformity along the spatial circle (i.e., Gregory-Laflamme instability) and determine the order of the associated phase transition. For $3\le d<4$, we argue that at the critical mass, the uniform string star can transition into a localized black hole. More generally, we describe the sequence of transitions from a large uniform black string as its mass decreases, depending on the number of dimensions $d$. Additionally, using the $SL(2)_k/U(1)$ model in string theory, we show that for sufficiently large $d$, the uniform black string is stable against non-uniformity before transitioning into fundamental strings. We also present a novel solution that exhibits double winding symmetry breaking in the asymptotically $\mathbb{R}^d\times\mathbb{S}^1_\tau\times\mathbb{S}^1_z$ Euclidean spacetime.

Tidal Love numbers of anti-de Sitter black holes are understood as linear response coefficients governing how the holographically dual plasma polarizes when the geometry of the space, in which the plasma lives, is deformed. So far, this picture has been applied only to black branes with plane wave perturbations. We fill the gap in the literature by performing the computation of tidal Love numbers for the four-dimensional Schwarzschild solution in global anti-de Sitter, which is dual to a conformal plasma on $S^2$. We conclude about the effect of the bulk gravitational perturbations on the boundary metric and stress tensor, responsible for the geometric polarization. The computation of the tidal Love numbers is performed in both Regge-Wheeler gauge and the Kodama-Ishibashi gauge-invariant approach. We spell out how to convert the tidal Love numbers determined in these two formalisms and find perfect agreement. We also relate the Kodama- Ishibashi formalism with the Kovtun-Starinets approach, which is particularly well suited for the holographic analysis of black branes. This allows us to compare with the tidal Love number results for black branes in anti-de Sitter, also finding agreement in the relevant regime.

Inhomogeneous quantum chains have recently been considered in the context of developing novel discrete realizations of holographic dualities. To advance this programme, we explore the ground states of infinite chains with large number $N$ of Majorana fermions on each site, which interact via on-site $q$-body Sachdev-Ye-Kitaev (SYK) couplings, as well as via additional inhomogeneous hopping terms between nearest-neighbour sites. The hopping parameters are either aperiodically or randomly distributed. Our approach unifies techniques to solve SYK-like models in the large $N$ limit with a real-space renormalization group method known as strong-disorder renormalization group (SDRG). We show that the SDRG decimation of SYK dots linked by a strong hopping induces an effective hopping interaction between their neighbouring sites. If two decimated sites are nearest neighbours, in the large $q$ limit their local ground states admit a holographic dual description in terms of eternal traversable wormholes. At the end of the SDRG procedure, we obtain a factorised ground state of the infinite inhomogeneous SYK chains that we consider, which has a spacetime description involving a sequence of wormholes. This amounts to a local near-boundary description of the bulk geometry in the context of discrete holography.

We compute the two-point function of protected dimension-1 operators in ABJM up to two loops in dimensional regularization. The result exhibits uniform transcendentality empirically, which we conjecture to hold at all orders. We leverage this property to streamline the reconstruction of the dimensional regularization expansion of master integrals in terms of bases of Euler sums of uniform transcendental weight.

We discuss unusual $\theta$ terms that can appear in field theories that allow global vortices. These `Cheshire $\theta$ terms' induce Aharonov-Bohm effects for some particles that move around vortices. For example, a Cheshire $\theta$ term can appear in QCD coupled to an axion and induces Aharonov-Bohm effects for baryons and leptons moving around axion strings.

The double copy relates gravitational theories to the square of gauge theories. While it is well understood in flat backgrounds, its precise realisation around curved spacetimes remains an open question. In this paper, we construct a classical double copy for cohomology class representatives in the minitwistor space of hyperbolic spacetimes. We find that the realisation of a physical double copy requires that the masses of the different spinning fields are not equal, contrary to the flat space prescription. This leads to a position-space double copy for bulk-to-boundary propagators. We also show that in coordinate space, this implies the Cotton double copy for waves and warped black holes of Topologically Massive Gravity. We show that these are exact double copy relations by constructing their Kerr-Schild metrics and also analysing the Kerr-Schild double copy. Furthermore, we find that near the boundary the double copy relates the dual CFT currents.

We initiate a study of the complexity of quantum field theories (QFTs) by proposing a measure of information contained in a QFT and its observables. We show that from minimal assertions, one is naturally led to measure complexity by two integers, called format and degree, which characterize the information content of the functions and domains required to specify a theory or an observable. The strength of this proposal is that it applies to any physical quantity, and can therefore be used for analyzing complexities within an individual QFT, as well as studying the entire space of QFTs. We discuss the physical interpretation of our approach in the context of perturbation theory, symmetries, and the renormalization group. Key applications include the detection of complexity reductions in observables, for example due to algebraic relations, and understanding the emergence of simplicity when considering limits. The mathematical foundations of our constructions lie in the framework of sharp o-minimality, which ensures that the proposed complexity measure exhibits general properties inferred from consistency and universality.

We demonstrate a precise relation between the rate of complexity of quantum states excited by local operators in two-dimensional conformal field theories and the radial momentum of particles in 3-dimensional Anti-de Sitter spacetimes. Similar relations have been anticipated based on qualitative models for operator growth. Here, we make this correspondence sharp with two key ingredients: the precise definition of quantum complexity given by the spread complexity of states, and the match of its growth rate to the bulk momentum measured in the proper radial distance coordinate.

We propose a novel strategy to fit experimental data using a UV complete amplitude ansatz satisfying the constraints of Analyticity, Crossing, and Unitarity. We focus on $\pi\pi$ scattering combining both experimental and lattice data. The fit strategy requires using S-matrix Bootstrap methods and non-convex Particle Swarm Optimization techniques. Using this procedure, we numerically construct a full-fledged scattering amplitude that fits the data and contains the known QCD spectrum that couples to $\pi \pi$ states below $1.4$ GeV. The amplitude constructed agrees below the two-particle threshold with the two-loop $\chi$PT prediction. Moreover, we correctly predict the $D_2$ phase shift, the appearance of a spin three state, and the behavior of the high-energy total cross-section. Finally, we find a genuine tetraquark resonance around 2 GeV, which we argue might be detected by looking into the decays of B mesons.

Quantum error correction (QEC) codes are fundamentally linked to quantum phases of matter: the degenerate ground state manifold corresponds to the code space, while topological excitations represent error syndromes. Building on this concept, the Sachdev-Ye-Kitaev (SYK) model, characterized by its extensive quasi-ground state degeneracy, serves as a constant rate approximate QEC code. In this work, we study the impacts of decoherence on the information-theoretic capacity of SYK models and their variants. Such a capacity is closely tied to traversable wormholes via its thermofield double state, which theoretically enables the teleportation of information across a black hole. We calculate the coherent information in the maximally entangled quasi-ground state space of the SYK models under the fermion parity breaking and parity conserving noise. Interestingly, we find that under the strong fermion parity symmetric noise, the mixed state undergoes the strong to weak spontaneous symmetry breaking of fermion parity, which also corresponds to the information-theoretic transition. Our results highlight the degradation of wormhole traversability in realistic quantum scenarios, as well as providing critical insights into the behavior of approximate constant-rate QEC codes under decoherence.

Scrambling unitary dynamics in a quantum system transmutes local quantum information into a non-local web of correlations which manifests itself in a complex spatio-temporal pattern of entanglement. In such a context, we show there can exist three distinct dynamical phases characterised by qualitatively different forms of quantum correlations between two disjoint subsystems of the system. Transitions between these phases are driven by the relative sizes of the subsystems and the degree scrambling that the dynamics effects. Besides a phase which has no quantum correlations as manifested by vanishing entanglement between the parts and a phase which has non-trivial quantum correlations quantified by a finite entanglement monotone, we reveal a new phase transition within the entangled phase which separates phases wherein the quantum correlations are invisible or visible to measurements on one of the subsystems. This is encoded in the qualitatively different properties of the ensemble of states on one of the subsystems conditioned on the various measurement outcomes on the other subsystem. This provides a new characterisation of entanglement phases in terms of their response to measurements instead of the more ubiquitous measurement-induced entanglement transitions. Our results have implications for the kind of tasks that can be performed using measurement feedback within the framework of quantum interactive dynamics.

We analyze the second order perturbations of the Deser-Woodard II (DWII), Vardanyan-Akrami-Amendola-Silvestri (VAAS) and Amendola-Burzilla-Nersisyan (ABN) nonlocal gravity models in an attempt to extract their associated gravitational wave energy-momentum fluxes. In Minkowski spacetime, the gravitational spatial momentum density is supposed to scale at most as $1/r^{2}$, in the $r \rightarrow \infty$ limit, where $r$ is the observer-source spatial distance. The DWII model has a divergent flux because its momentum density goes as $1/r$; though this can be avoided when we set to zero the first derivative of its distortion function at the origin. Meanwhile, the ABN model also suffers from a divergent flux because its momentum density goes as $r^{2}$. The momentum density from the VAAS model was computed on a cosmological background expressed in a Fermi-Normal-Coordinate system, and was found to scale as $r$. For generic parameters, therefore, none of these three Dark Energy models appear to yield well-defined gravitational wave energies, as a result of their nonlocal gravitational self-interactions.

We develop a relativistic framework of integral quantization applied to the motion of spinless particles in the four-dimensional Minkowski spacetime. The proposed scheme is based on coherent states generated by the action of the Heisenberg-Weyl group and has been motivated by the Hamiltonian description of the geodesic motion in General Relativity. We believe that this formulation should also allow for a generalization to the motion of test particles in curved spacetimes. A key element in our construction is the use of suitably defined positive operator-valued measures. We show that this approach can be used to quantize the one-dimensional nonrelativistic harmonic oscillator, recovering the standard Hamiltonian as obtained by the canonical quantization. Our formalism is then applied to the Hamiltonian associated with the motion of a relativistic particle in the Minkowski spacetime. A direct application of our model, including a computation of transition amplitudes between states characterized by fixed positions and momenta, is postponed to a forthcoming article.

We summarise highlights from an ongoing research programme that aims, in the long run, at the ambitious goal of building a realistic, complete holographic composite-Higgs model. This contribution focuses on vacuum misalignment, by showing how to unify its description, as a phenomenon arising from weak coupling considerations, in the holographic description of a strongly coupled field theory in terms of a dual gravity theory. This is achieved by a non-trivial treatment of boundary-localised terms in the gravity action. The gravity backgrounds considered are completely regular and smooth. We provide numerical examples showing that the mass spectrum of particles in the four-dimensional theory is free of pathologies, and that a small hierarchy arises naturally, between the light states that, in this simplified set up, are analogous to the standard-model particles, and all the other, new composite states emerging in the strongly coupled theory.

We compute the (displacement) gravitational wave memory due to a quasicircular inspiral of two black holes using a variety of perturbative techniques. Within post-Newtonian theory, we extend previous results for non-spinning binaries to 3.5PN order. Using the gravitational self-force approach, we compute the memory at first order in the mass ratio for inspirals into a Kerr black hole. We do this both numerically and via a double post-Newtonian--self-force expansion which we carry out to 5PN order. At second order in the self-force approach, near-zone calculations encounter an infrared divergence associated with memory, which is resolved through matching the near-zone solution to a post-Minkowskian expansion in the far zone. We describe that matching procedure for the first time and show how it introduces nonlocal-in-time memory effects into the two-body dynamics at second order in the mass ratio, as was also predicted by recent 5PN calculations within the effective field theory approach. We then compute the gravitational-wave memory through second order in the mass ratio (excluding certain possible memory distortion effects) and find that it agrees well with recent results from numerical relativity simulations for near-comparable-mass binaries.

Violating the slow-roll regime during the final stages of inflation can significantly enhance curvature perturbations, a scenario often invoked in models producing primordial black holes and small-scale scalar induced gravitational waves. When perturbations are enhanced, one approaches the regime in which tree-level computations are insufficient, and nonlinear corrections may become relevant. In this work, we conduct lattice simulations of ultra-slow-roll (USR) dynamics to investigate the significance of nonlinear effects, both in terms of backreaction on the background and in the evolution of perturbations. Our systematic study of various USR potentials reveals that nonlinear corrections are significant when the tree-level curvature power spectrum peaks at $\mathcal{P}^{\rm max}_{\zeta} = {\cal O}(10^{-3})-{\cal O}(10^{-2})$, with 5%$-$10% corrections. Larger enhancements yield even greater differences. We establish a universal relation between simulation and tree-level quantities $\dot\phi = \dot\phi_{\rm tree}\left(1+\sqrt{\mathcal{P}^{\rm max}_{\zeta,\rm tree}}\right)$ at the end of the USR phase, which is valid in all cases we consider. Additionally, we explore how nonlinear interactions during the USR phase affect the clustering and non-Gaussianity of scalar fluctuations, crucial for understanding the phenomenological consequences of USR, such as scalar-induced gravitational waves and primordial black holes. Our findings demonstrate the necessity of going beyond leading order perturbation theory results, through higher-order or non-perturbative computations, to make robust predictions for inflation models exhibiting a USR phase.