Search for: All records

A<sc>bstract</sc> By adapting previously known arguments concerning Ricci flow and thec-theorem, we give a direct proof that in a two-dimensional sigma-model with compact target space, scale invariance implies conformal invariance in perturbation theory. This argument, which applies to a general sigma-model constructed with a target space metric andB-field, is in accord with a more general proof in the literature that applies to arbitrary two-dimensional quantum field theories. Models with extended supersymmetry and aB-field are known to provide interesting test cases for the relation between scale invariance and conformal invariance in sigma-model perturbation theory. We give examples showing that in such models, the obstructions to conformal invariance suggested by general arguments can actually occur in models with target spaces that are not compact or complete. Thus compactness of the target space, or at least a suitable condition of completeness, is necessary as well as sufficient to ensure that scale invariance implies conformal invariance in models of this type. 

Abstract We discuss high energy properties of states for (possibly interacting) quantum fields in curved spacetimes. In particular, if the spacetime is real analytic, we show that an analogue of the timelike tube theorem and the Reeh–Schlieder property hold with respect to states satisfying a weak form of microlocal analyticity condition. The former means the von Neumann algebra of observables of a spacelike tube equals the von Neumann algebra of observables of a significantly bigger region that is obtained by deforming the boundary of the tube in a timelike manner. This generalizes theorems by Araki (Helv Phys Acta 36:132–139, 1963) and Borchers (Nuovo Cim (10) 19:787–793, 1961) to curved spacetimes. 

A<sc>bstract</sc> We conjecture a formula for the spectral form factor of a double-scaled matrix integral in the limit of large time, large density of states, and fixed temperature. The formula has a genus expansion with a nonzero radius of convergence. To understand the origin of this series, we compare to the semiclassical theory of “encounters” in periodic orbits. In Jackiw-Teitelboim (JT) gravity, encounters correspond to portions of the moduli space integral that mutually cancel (in the orientable case) but individually grow at low energies. At genus one we show how the full moduli space integral resolves the low energy region and gives a finite nonzero answer. 

Abstract We investigate the differential geometry of the moduli space of instantons on ${\mathrm{S}}^3\times {\mathrm{S}}^1$. Extending previous results, we show that a sigma-model with this target space can be expected to possess a large $N=4$superconformal symmetry, supporting speculations that this sigma-model may be dual to Type IIB superstring theory on ${\mathrm{AdS}}_3\times {\mathrm{S}}^3\times {\mathrm{S}}^3\times {\mathrm{S}}^1$. The sigma-model is parametrized by three integers—the rank of the gauge group, the instanton number, and a ‘level’ (the integer coefficient of a topologically nontrivialB-field, analogous to a WZW level). These integers are expected to correspond to two five-brane charges and a one-brane charge. The sigma-model is weakly coupled when the level, conjecturally corresponding to one of the five-brane changes, becomes very large, keeping the other parameters fixed. The central charges of the large $N=4$algebra agree, at least semiclassically, with expectations from the duality. 

A<sc>bstract</sc> We establish an equivalence between two different quantum quench problems, the joining local quantum quench and the Möbius quench, in the context of (1 + 1)-dimensional conformal field theory (CFT). Here, in the former, two initially decoupled systems (CFTs) on finite intervals are joined att= 0. In the latter, we consider the system that is initially prepared in the ground state of the regular homogeneous Hamiltonian on a finite interval and, aftert= 0, let it time-evolve by the so-called Möbius Hamiltonian that is spatially inhomogeneous. The equivalence allows us to relate the time-dependent physical observables in one of these problems to those in the other. As an application of the equivalence, we construct a holographic dual of the Möbius quench from that of the local quantum quench. The holographic geometry involves an end-of-the-world brane whose profile exhibits non-trivial dynamics. 

A<sc>bstract</sc> We propose an algebra of operators along an observer’s worldline as a background-independent algebra in quantum gravity. In that context, it is natural to think of the Hartle-Hawking no boundary state as a universal state of maximum entropy, and to define entropy in terms of the relative entropy with this state. In the case that the only spacetimes considered correspond to de Sitter vacua with different values of the cosmological constant, this definition leads to sensible results. 

A<sc>bstract</sc> We explore a large class of correlation measures called theα−zRényi mutual informations (RMIs). Unlike the commonly used notion of RMI involving linear combinations of Rényi entropies, theα−zRMIs are positive semi-definite and monotonically decreasing under local quantum operations, making them sensible measures of total (quantum and classical) correlations. This follows from their descendance from Rényi relative entropies. In addition to upper bounding connected correlation functions between subsystems, we prove the much stronger statement that for certain values ofαandz, theα−zRMIs also lower bound certain connected correlation functions. We develop an easily implementable replica trick which enables us to compute theα−zRMIs in a variety of many-body systems including conformal field theories, free fermions, random tensor networks, and holography. 

A<sc>bstract</sc> The gravitational path integral can be used to compute the number of black hole states for a given energy window, or the free energy in a thermal ensemble. In this article we explain how to use the gravitational path integral to compute the separate number of bosonic and fermionic black hole microstates. We do this by comparing the partition function with and without the insertion of (−1)^F. In particular we introduce a universal rotating black hole that contributes to the partition function in the presence of (−1)^F. We study this problem for black holes in asymptotically flat space and in AdS, putting constraints on the high energy spectrum of holographic CFTs (not necessarily supersymmetric). Finally, we analyze wormhole contributions to related quantities. 

A<sc>bstract</sc> We propose a new formula for computing holographic Renyi entropies in the presence of multiple extremal surfaces. Our proposal is based on computing the wave function in the basis of fixed-area states and assuming a diagonal approximation for the Renyi entropy. For Renyi indexn≥ 1, our proposal agrees with the existing cosmic brane proposal for holographic Renyi entropy. Forn <1, however, our proposal predicts a new phase with leading order (in Newton’s constantG) corrections to the cosmic brane proposal, even far from entanglement phase transitions and when bulk quantum corrections are unimportant. Recast in terms of optimization over fixed-area states, the difference between the two proposals can be understood to come from the order of optimization: forn <1, the cosmic brane proposal is a minimax prescription whereas our proposal is a maximin prescription. We demonstrate the presence of such leading order corrections using illustrative examples. In particular, our proposal reproduces existing results in the literature for the PSSY model and high-energy eigenstates, providing a universal explanation for previously found leading order corrections to then <1 Renyi entropies. 

A<sc>bstract</sc> It is difficult to construct a post-inflation QCD axion model that solves the axion quality problem (and hence the Strong CP problem) without introducing a cosmological disaster. In a post-inflation axion model, the axion field value is randomized during the Peccei-Quinn phase transition, and axion domain walls form at the QCD phase transition. We emphasize that the gauge equivalence of all minima of the axion potential (i.e., domain wall number equals one) is insufficient to solve the cosmological domain wall problem. The axion string on which a domain wall ends must exist as an individual object (as opposed to a multi-string state), and it must be produced in the early universe. These conditions are often not satisfied in concrete models. Post-inflation axion models also face a potential problem from fractionally charged relics; solving this problem often leads to low-energy Landau poles for Standard Model gauge couplings, reintroducing the quality problem. We study several examples, finding that models that solve the quality problem face cosmological problems, and vice versa. This is not a no-go theorem; nonetheless, we argue that it is much more difficult than generally appreciated to find a viable post-inflation QCD axion model. Successful examples may have a nonstandard cosmological history (e.g., multiple types of cosmic axion strings of different tensions), undermining the widespread expectation that the post-inflation QCD axion scenario predicts a unique mass for axion dark matter.