Recently, Altavista, Anastasi, Angius and Uranga discussed a method to construct junctions and bouquets of different perturbative string theories. Following this analysis, we here argue that three non-tachyonic ten-dimensional heterotic string theories can be joined together at a nine-dimensional junction.

Japan

Yuji Tachikawa

On the trivalent junction of three non-tachyonic heterotic string theories

We study aspects of the AdS/CFT correspondence for $$ \mathcal{N}=4 $$ U($\textit{N}$) super Yang-Mills theory on $\textit{S}$ $\textit{/}$Γ, where Γ ⊂ SU(2) is a finite subgroup leading to an ADE singularity in the bulk AdS geometry. We show that a large vacuum degeneracy arises from the choice of gauge holonomy on $\textit{S}$ $\textit{/}$Γ. On the gravity side, we argue that the bulk ADE singularity supports topological degrees of freedom responsible for this degeneracy. We then provide a holographic derivation of a corresponding large vacuum degeneracy for class S theories of type U($\textit{N}$), showing that these topological degrees of freedom admit an effective description in terms of a three-dimensional level-$\textit{N}$ Chern-Simons theory, whose gauge group G is determined by Γ. Finally, we discuss how the one-form symmetries of the $$ \mathcal{N}=4 $$ super Yang-Mills theory are realized on the Chern-Simons theory side.

Sunjin Choi

On holography with ADE singularities

We point out that fermionic unitary operators which anticommute among themselves appear in various situations in quantum field theories with anomalies in the Hamiltonian formalism. To illustrate, we give multiple derivations of the fact that position-dependent U(1) transformations of two-dimensional theories with U(1) symmetry of odd level are fermionic when the winding number is odd. We then relate this mechanism to the anomalies of the discrete ℤ ⊂ U(1) symmetry, whose description also crucially uses unitary operators which are fermionic. We also show that position-dependent SU(2) transformations of four-dimensional theories with SU(2) symmetry with Witten anomaly are fermionic and anticommute among themselves when the winding number is odd.

Masaki Okada

Shutaro Shimamura

Yi Zhang

On anomalies and fermionic unitary operators

A uniform construction of non-supersymmetric 0-, 4-, 6- and 7-branes in heterotic string theory was announced and outlined in our letter [61]. In this full paper, we provide details on their properties. Among other things, we discuss the charges carried by the branes, their topological and dynamical stability, the exact worldsheet descriptions of their near-horizon regions, and the relationship of the branes to the mathematical notion of topological modular forms.

Justin Kaidi

Kazuya Yonekura

On non-supersymmetric heterotic branes

Noninvertible symmetries of quantum field theories and many-body systems generalize the concept of symmetries by allowing noninvertible operations in addition to more ordinary invertible ones described by groups. The aim of this Letter is to point out that these noninvertible symmetries act on local operators by quantum operations, i.e., completely positive maps between density matrices, which form a natural class of operations containing both unitary evolutions and measurements and play an important role in quantum information theory. This observation will be illustrated by the Kramers-Wannier duality of the one-dimensional quantum Ising chain, which is a prototypical example of noninvertible symmetry operations.

Noninvertible Symmetries Act Locally by Quantum Operations

The common statement that any consistent quantum gravity theory contains dynamical objects with all possible charges suggests that there are still a number of hitherto-unidentified branes in string theory. Here we give the exact worldsheet description of near-horizon limits of nonsupersymmetric <math><mi>p</mi></math>-branes in ten-dimensional <math><mtext>Spin</mtext><mo>(</mo><mn>32</mn><mo>)</mo><mo>/</mo><msub><mi>Z</mi><mn>2</mn></msub></math> or <math><mo>(</mo><msub><mi>E</mi><mn>8</mn></msub><mo>×</mo><msub><mi>E</mi><mn>8</mn></msub><mo>)</mo><mo>⋊</mo><msub><mi>Z</mi><mn>2</mn></msub></math> heterotic superstring theories for <math><mi>p</mi><mo>=</mo><mn>7</mn></math>, 6, 4, 0.

United States

Kantaro Ohmori

Nonsupersymmetric Heterotic Branes

We introduce a class of 3d theories consisting of strongly-coupled   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4 systems coupled to   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 3 Chern-Simons gauge multiplets, which exhibit   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4 enhancements when a peculiar condition on the Chern-Simons levels is met. An example is the SU(N)3 Chern-Simons theory coupled to the 3d T  N  theory, which enhances to   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4 when 1/k 1 + 1/k 2 + 1/k 3 = 0. We also show that some but not all of these   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4 enhancements can be understood by considering M5-branes on a special class of Seifert manifolds. Our construction provides a large class of   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4 theories which have not been studied previously.

France

Benjamin Assel

Italy

Alessandro Tomasiello

On   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4 supersymmetry enhancements in three dimensions

It is known that the asymptotic density of states of a 2d CFT in an irreducible representation ρ of a finite symmetry group G is proportional to (dim ρ)2. We show how this statement can be generalized when the symmetry can be non-invertible and is described by a fusion category   <math> <mi>C</mi> </math>  $$ \mathcal{C} $$ . Along the way, we explain what plays the role of a representation of a group in the case of a fusion category symmetry; the answer to this question is already available in the broader mathematical physics literature but not yet widely known in hep-th. This understanding immediately implies a selection rule on the correlation functions, and also allows us to derive the asymptotic density.

Ying-Hsuan Lin

Sahand Seifnashri

Asymptotic density of states in 2d CFTs with non-invertible symmetries

We argue that having an odd number of Majorana fermion zero modes on a dynamical point-like soliton signifies an inconsistency in a theory with 3+1 and higher dimensions. We check this statement in a couple of examples in field theory and in string/M theory.

Yotaro Sato

Taizan Watari

On odd number of fermion zero modes on solitons in quantum field theory and string/M theory

We study higher symmetries and anomalies of 4d   <math> <mi>so</mi> </math>  $$ \mathfrak{so} $$ (2n  c ) gauge theory with 2n  f  flavors. We find that they depend on the parity of n  c  and n  f , the global form of the gauge group, and the discrete theta angle. The contribution from the fermions plays a central role in our analysis. Furthermore, our conclusion applies to   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 1 supersymmetric cases as well, and we see that higher symmetries and anomalies match across the Intriligator-Seiberg duality between   <math> <mi>so</mi> </math>  $$ \mathfrak{so} $$ (2n  c ) ↔   <math> <mi>so</mi> </math>  $$ \mathfrak{so} $$ (2n  f  − 2n  c  + 4).