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We discuss a set of heterotic and type II string theory compactifications to$$1+1$$$1+1$dimensions that are characterized by factorized internal worldsheet CFTs of the form$$V_1\otimes \bar{V}_2$$$V_1\otimes {\overline{V}}_2$, where$$V_1, V_2$$$V_1,V_2$are self-dual (super) vertex operator algebras. In the cases with spacetime supersymmetry, we show that the BPS states form a module for a Borcherds–Kac–Moody (BKM) (super)algebra, and we prove that for each model the BKM (super)algebra is a symmetry of genus zero BPS string amplitudes. We compute the supersymmetric indices of these models using both Hamiltonian and path integral formalisms. The path integrals are manifestly automorphic forms closely related to the Borcherds–Weyl–Kac denominator. Along the way, we comment on various subtleties inherent to these low-dimensional string compactifications.

 

A bstract We describe an algebra of observables for a static patch in de Sitter space, with operators gravitationally dressed to the worldline of an observer. The algebra is a von Neumann algebra of Type II 1 . There is a natural notion of entropy for a state of such an algebra. There is a maximum entropy state, which corresponds to empty de Sitter space, and the entropy of any semiclassical state of the Type II 1 algebras agrees, up to an additive constant independent of the state, with the expected generalized entropy S gen = ( A/ 4 G N ) + S out . An arbitrary additive constant is present because of the renormalization that is involved in defining entropy for a Type II 1 algebra. 

A bstract Black hole event horizons and cosmological event horizons share many properties, making it natural to ask whether our recent advances in understanding black holes generalize to cosmology. To this end, we discuss a paradox that occurs if observers can access what lies beyond their cosmological horizon in the same way that they can access what lies beyond a black hole horizon. In particular, distinct observers with distinct horizons may encode the same portion of spacetime, violating the no-cloning theorem of quantum mechanics. This paradox is due precisely to the observer-dependence of the cosmological horizon — the sharpest difference from a black hole horizon — although we will argue that the gravity path integral avoids the paradox in controlled examples. 

Abstract We consider quantum chaos diagnostics of the variational circuit states at random parameters and explore their connection to the circuit expressibility and optimizability. By measuring the operator spreading coefficient and the eigenvalue spectrum of the modular Hamiltonian of the reduced density matrix, we identify the emergence of universal random matrix ensembles in high-depth circuit states. The diagnostics that use the eigenvalue spectrum, e.g. operator spreading and entanglement entropy, turn out to be more accurate measures of the variational quantum algorithm optimization efficiency than those that use the level spacing distribution of the entanglement spectrum, such as r -statistics or spectral form factors. 

A bstract We discuss aspects of the possible transition between small black holes and highly excited fundamental strings. We focus on the connection between black holes and the self gravitating string solution of Horowitz and Polchinski. This solution is interesting because it has non-zero entropy at the classical level and it is natural to suspect that it might be continuously connected to the black hole. Surprisingly, we find a different behavior for heterotic and type II cases. For the type II case we find an obstruction to the idea that the two are connected as classical solutions of string theory, while no such obstruction exists for the heterotic case. We further provide a linear sigma model analysis that suggests a continuous connection for the heterotic case. We also describe a solution generating transformation that produces a charged version of the self gravitating string. This provides a fuzzball-like construction of near extremal configurations carrying fundamental string momentum and winding charges. We provide formulas which are exact in α ′ relating the thermodynamic properties of the charged and the uncharged solutions. 

A bstract We study $$ \mathcal{N} $$ N = 2 supersymmetric Sachdev-Ye-Kitaev (SYK) models with com- plex fermions at non-zero background charge. Motivated by multi-charge supersymmetric black holes, we propose a new $$ \mathcal{N} $$ N = 2 SYK model with multiple U (1) symmetries, integer charges, and a non-vanishing supersymmetric index, realizing features not present in known SYK models. In both models, a conformal solution with a super-Schwarzian mode emerges at low temperatures, signalling the appearance of nearly AdS 2 /BPS physics. However, in contrast to complex SYK, the fermion scaling dimension depends on the background charge in the conformal limit. For a critical charge, we find a high to low entropy phase transition in which the conformal solution ceases to be valid. This transition has a simple interpretation– the fermion scaling dimension violates the unitarity bound. We offer some comments on a holographic interpretation for supersymmetric black holes. 

A bstract Recently Leutheusser and Liu [1, 2] identified an emergent algebra of Type III 1 in the operator algebra of $$ \mathcal{N} $$ N = 4 super Yang-Mills theory for large N . Here we describe some 1/ N corrections to this picture and show that the emergent Type III 1 algebra becomes an algebra of Type II ∞ . The Type II ∞ algebra is the crossed product of the Type III 1 algebra by its modular automorphism group. In the context of the emergent Type II ∞ algebra, the entropy of a black hole state is well-defined up to an additive constant, independent of the state. This is somewhat analogous to entropy in classical physics. 

A bstract We consider a Hayden & Preskill like setup for both maximally chaotic and sub-maximally chaotic quantum field theories. We act on the vacuum with an operator in a Rindler like wedge R and transfer a small subregion I of R to the other wedge. The chaotic scrambling dynamics of the QFT Rindler time evolution reveals the information in the other wedge. The holographic dual of this process involves a particle excitation falling into the bulk and crossing into the entanglement wedge of the complement to r = R\I . With the goal of studying the locality of the emergent holographic theory we compute various quantum information measures on the boundary that tell us when the particle has entered this entanglement wedge. In a maximally chaotic theory, these measures indicate a sharp transition where the particle enters the wedge exactly when the insertion is null separated from the quantum extremal surface for r . For sub-maximally chaotic theories, we find a smoothed crossover at a delayed time given in terms of the smaller Lyapunov exponent and dependent on the time-smearing scale of the probe excitation. The information quantities that we consider include the full vacuum modular energy R\I as well as the fidelity between the state with the particle and the state without. Along the way, we find a new explicit formula for the modular Hamiltonian of two intervals in an arbitrary 1+1 dimensional CFT to leading order in the small cross ratio limit. We also give an explicit calculation of the Regge limit of the modular flowed chaos correlator and find examples which do not saturate the modular chaos bound. Finally, we discuss the extent to which our results reveal properties of the target of the probe excitation as a “stringy quantum extremal surface” or simply quantify the probe itself thus giving a new approach to studying the notion of longitudinal string spreading.