 Award ID(s):
 1915093
 Publication Date:
 NSFPAR ID:
 10164110
 Journal Name:
 Communications in Mathematical Physics
 ISSN:
 00103616
 Sponsoring Org:
 National Science Foundation
More Like this

A bstract We investigate the admissible vectorvalued modular forms having three independent characters and vanishing Wronskian index and determine which ones correspond to genuine 2d conformal field theories. This is done by finding bilinear cosettype relations that pair them into meromorphic characters with central charges 8, 16, 24, 32 and 40. Such pairings allow us to identify some characters with definite CFTs and rule out others. As a key result we classify all unitary threecharacter CFT with vanishing Wronskian index, excluding c = 8, 16. The complete list has two infinite affine series B r ,1 , D r ,1 and 45 additional theories. As a byproduct, at higher values of the total central charge we also find constraints on the existence or otherwise of meromorphic theories. We separately list several cases that potentially correspond to Intermediate Vertex Operator Algebras.

A bstract There is a wellknown map from 4d $$ \mathcal{N} $$ N = 2 superconformal field theories (SCFTs) to 2d vertex operator algebras (VOAs). The 4d Schur index corresponds to the VOA vacuum character, and must be a solution with integral coefficients of a modular differential equation. This suggests a classification program for 4d $$ \mathcal{N} $$ N = 2 SCFTs that starts with modular differential equations and proceeds by imposing all known constraints that follow from the 4d → 2d map. This program becomes fully algorithmic once one specifies the order of the modular differential equation and the rank (complex dimension of the Coulomb branch) of the $$ \mathcal{N} $$ N = 2 theory. As a proof of concept, we apply the algorithm to the study of ranktwo $$ \mathcal{N} $$ N = 2 SCFTs whose Schur indices satisfy a fourthorder untwisted modular differential equation. Scanning over a large number of putative cases, only 15 satisfy all of the constraints imposed by our algorithm, six of which correspond to known 4d SCFTs. More sophisticated constraints can be used to argue against the existence of the remaining nine cases. Altogether, this indicates that our knowledge of such ranktwo SCFTsmore »

Abstract We discuss a set of heterotic and type II string theory compactifications to
dimensions that are characterized by factorized internal worldsheet CFTs of the form$$1+1$$ $1+1$ , where$$V_1\otimes \bar{V}_2$$ ${V}_{1}\otimes {\overline{V}}_{2}$ are selfdual (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 lowdimensional string compactifications.$$V_1, V_2$$ ${V}_{1},{V}_{2}$ 
A bstract We study the large charge sector of the defect CFT defined by the halfBPS Wilson loop in planar N = 4 supersymmetric YangMills theory. Specifically, we consider correlation functions of two large charge insertions and several light insertions in the doublescaling limit where the ’t Hooft coupling λ and the large charge J are sent to infinity, with the ratio J/ $$ \sqrt{\lambda } $$ λ held fixed. They are holographically dual to the expectation values of light vertex operators on a classical string solution with large angular momentum, which we evaluate in the leading large J limit. We also compute the twopoint function of large charge insertions by evaluating the onshell string action, supplemented by the boundary terms that generalize the one introduced by Drukker, Gross and Ooguri for the Wilson loop without insertions. For a special class of correlation functions, we reproduce the string results from field theory by using supersymmetric localization. The results are given by correlation functions in an “emergent” matrix model whose matrix size is proportional to J and whose spectral curve coincides with that of the classical string. Similar matrix models appeared in the study of extremal correlators in rank1 $$ \mathcal{N}more »

A bstract We consider a Hayden & Preskill like setup for both maximally chaotic and submaximally 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 submaximally chaotic theories, we find a smoothed crossover at a delayed time given in terms of the smaller Lyapunov exponent and dependent on the timesmearing scale of the probe excitation. The information quantities that we consider include the full vacuum modular energy R\I asmore »