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On hydrogen-like bound states in \( \mathcal{N} \) = 4 super Yang-Mills

Using relativistic quantum mechanics, we study the spectrum of a non-BPS two-particle bound state in the massive phase of \( \mathcal{N} \) = 4 super Yang-Mills, in the limit when one of the particles is infinitely heavier than the other. We find that the spectrum shows the exact n 2 degeneracy for each principal quantum number n, just as in the strict non-relativistic limit. This ...

Anomaly of strings of 6d \( \mathcal{N}=\left(1,0\right) \) theories

We obtain the anomaly polynomial of strings of general 6d \( \mathcal{N}=\left(1,0\right) \) theories in terms of anomaly inflow. Our computation sheds some light on the reason why the simplest 6d \( \mathcal{N}=\left(1,0\right) \) theory has E 8 flavor symmetry, and also partially explains a curious numerology in F-theory.

Frozen singularities in M and F theory

We revisit the duality between ALE singularities in M-theory and 7-branes on a circle in F-theory. We see that a frozen M-theory singularity maps to a circle compactification involving a rotation of the plane transverse to the 7-brane, showing an interesting correspondence between commuting triples in simply-laced groups and Kodaira’s classification of singular elliptic fibrations. ...

Gauge interactions and topological phases of matter

We study the effects of strongly coupled gauge interactions on the properties of the topological phases of matter. In particular, we discuss fermionic systems with three spatial dimensions, protected by time-reversal symmetry. We first derive a sufficient condition for the introduction of a dynamical Yang–Mills field to preserve the topological phase of matter, and then show how ...

On 4d rank-one \( \mathcal{N}=3 \) superconformal field theories

We study the properties of 4d \( \mathcal{N}=3 \) superconformal field theories whose rank is one, i.e. those that reduce to a single vector multiplet on their moduli space of vacua. We find that the moduli space can only be of the form ℂ3/ℤ ℓ for ℓ=1, 2, 3, 4, 6, and that the supersymmetry automatically enhances to \( \mathcal{N}=4 \) for ℓ=1, 2. In addition, we determine the ...

4d \( \mathcal{N}=1 \) from 6d \( \mathcal{N}=\left(1,0\right) \) on a torus with fluxes

Compactifying \( \mathcal{N}=\left(1,0\right) \) theories on a torus, with additional fluxes for global symmetries, we obtain \( \mathcal{N}=1 \) supersymmetric theories in four dimensions. It is shown that for many choices of flux these models are toric quiver gauge theories with singlet fields. In particular we compare the anomalies deduced from the description of the ...

S-folds and 4d \( \mathcal{N} \) = 3 superconformal field theories

S-folds are generalizations of orientifolds in type IIB string theory, such that the geometric identifications are accompanied by non-trivial S-duality transformations. They were recently used by García-Etxebarria and Regalado to provide the first construction of four dimensional \( \mathcal{N} \) =3 superconformal theories. In this note, we classify the different variants of these ...

A review of the TN theory and its cousins

The $T_N$ theory is a four-dimensional $\mathcal {N} = 2$ superconformal field theory that has played a central role in the analysis of supersymmetric dualities in the last few years. The aim of this review is to collect known properties of the $T_N$ theory and its cousins in one place as a quick reference.

Instanton operators and symmetry enhancement in 5D supersymmetric gauge theories

Supersymmetric gauge theories in five dimensions often exhibit less symmetry than the ultraviolet fixed points from which they flow. The fixed points might have larger flavor symmetry or they might even be secretly 6D theories on $S^{1}$. Here we provide a simple criterion when such symmetry enhancement in the ultraviolet should occur, by a direct study of the fermionic zero modes ...

Magnetic discrete gauge field in the confining vacua and the supersymmetric index

It has recently been argued that the confining vacua of Yang-Mills theory in the far infrared can have topological degrees of freedom given by magnetic \( {\mathbb{Z}}_q \) gauge field, both in the non-supersymmetric case and in the \( \mathcal{N}=1 \) supersymmetric case. In this short note we give another piece of evidence by computing and matching the supersymmetric index of the ...

On skein relations in class S theories

Tachikawa 3 Department of Physics, Faculty of Science Loop operators of a class S theory arise from networks on the corresponding Riemann surface, and their operator product expansions are given in terms of

Moduli spaces of SO(8) instantons on smooth ALE spaces as Higgs branches of 4d \( \mathcal{N} \) = 2 supersymmetric theories

Yuji Tachikawa 0 0 Department of Physics, Faculty of Science, University of Tokyo , Bunkyo-ku, Tokyo 133-0022 , Japan Institute for the Physics and Mathematics of the Universe, University of Tokyo

On the 6d origin of discrete additional data of 4d gauge theories

Yuji Tachikawa 0 0 Department of Physics, Faculty of Science, University of Tokyo , Bunkyo-ku, Tokyo 133-0022 , Japan Institute for the Physics and Mathematics of the Universe, University of Tokyo

6d \( \mathcal{N}=\left(1,\;0\right) \) theories on S 1 /T 2 and class S theories: part II

We study the T 2 compactification of a class of 6d \( \mathcal{N}=\left(1,\;0\right) \) theories that is Higgsable to \( \mathcal{N}=\left(2,\;0\right) \) theories. We show that the resulting 4d \( \mathcal{N}=2 \) theory at the origin of the Coulomb branch and the parameter space is generically given by two superconformal matter sectors coupled by an infrared-free gauge multiplet ...

Gaiotto duality for the twisted A 2N −1 series

We study 4D \( \mathcal{N} \) = 2 superconformal theories that arise from the compactification of 6D \( \mathcal{N} \) = (2, 0) theories of type A 2N −1 on a Riemann surface C, in the presence of punctures twisted by a ℤ2 outer automorphism. We describe how to do a complete classification of these SCFTs in terms of three-punctured spheres and cylinders, which we do explicitly for A ...

Mass-deformed T N as a linear quiver

The T N theory is a non-Lagrangian theory with SU(N)3 flavor symmetry. We argue that when mass terms are given so that two of SU(N)’s are both broken to SU(N −1)×U(1), it becomes T N −1 theory coupled to an SU(N −1) vector multiplet together with N fundamentals. This implies that when two of SU(N)’s are both broken to U(1) N −1, the theory becomes a linear quiver. We perform ...

4d partition function on S1 × S3 and 2d Yang–Mills with nonzero area

Yuji Tachikawa 0 1 Subject Index 0 Department of Physics, Faculty of Science, University of Tokyo , Bunkyo, Tokyo 113-0033, Japan 1 Kavli Institute for the Physics and Mathematics of the Universe

6d \( \mathcal{N}=\left(1,0\right) \) theories on T 2 and class S theories. Part I

We show that the \( \mathcal{N}=\left(1,0\right) \) superconformal theory on a single M5 brane on the ALE space of type G = A n , D n , E n , when compactified on T 2, becomes a class S theory of type G on a sphere with two full punctures and a simple puncture. We study this relation from various viewpoints. Along the way, we develop a new method to study the 4d SCFT arising from ...

Anomaly polynomial of E-string theories

We determine the anomaly polynomial of the E-string theory and its higher-rank generalizations, that is, the 6d \( \mathcal{N} \) = (1, 0) superconformal theories on the worldvolume of one or multiple M5-branes embedded within the end-of-the-world brane with E 8 symmetry.

Anomaly polynomial of general 6D SCFTs

We describe a method to determine the anomaly polynomials of general 6D $\mathcal {N}={(2,0)}$ and $\mathcal {N}={(1,0)}$ superconformal field theories (SCFTs), in terms of the anomaly matching on their tensor branches. This method is almost purely field theoretical, and can be applied to all known 6D SCFTs. We demonstrate our method in many concrete examples, including $\mathcal ...