Advanced search

Loading...

Advanced search    

Search: authors:"Yuji Tachikawa"

32 papers found.
Use AND, OR, NOT, +word, -word, "long phrase", (parentheses) to fine-tune your search.

A study of time reversal symmetry of abelian anyons

Abstract We perform a study of time reversal symmetry of abelian anyons \( \mathcal{A} \) in 2+1 dimensions, in the spin structure independent cases. We will find the importance of the group \( \mathcal{C} \) of time-reversal-symmetric anyons modulo anyons composed from an anyon and its time reversal. Possible choices of local Kramers degeneracy are given by quadratic refinements...

Comments on the twisted punctures of Aeven class S theory

Abstract We point out that the USp symmetry associated to a full twisted puncture of a class S theory of type Aeven has the global anomaly associated to π4(USp) = ℤ2. We discuss manifestations of this fact in the context of the superconformal field theory R2,2N introduced by Chacaltana, Distler and Trimm. For example, we find that this theory can be thought of as a natural...

Anomalies involving the space of couplings and the Zamolodchikov metric

The anomaly polynomial of a theory can involve not only curvature two-forms of the flavor symmetry background but also two-forms on the space of coupling constants. As an example, we point out that there is a mixed anomaly between the R-symmetry and the topology of the space of exactly marginal couplings of class S theories. Using supersymmetry, we translate this anomaly to the K...

Anomaly matching on the Higgs branch

We point out that we can almost always determine by the anomaly matching the full anomaly polynomial of a supersymmetric theory in 2d, 4d or 6d if we assume that its Higgs branch is the one-instanton moduli space of some group G. This method not only provides by far the simplest method to compute the central charges of known theories of this class, e.g. 4d E 6,7,8 theories of...

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...

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.

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...

E 8 instantons on type-A ALE spaces and supersymmetric field theories

We consider the 6d superconformal field theory realized on M5-branes probing the E 8 end-of-the-world brane on the deformed and resolved ℂ 2/ℤ k singularity. We give an explicit algorithm which determines, for arbitrary holonomy at infinity, the 6d quiver gauge theory on the tensor branch, the type-A class S description of the T 2 compactification, and the star-shaped quiver...

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...

8d gauge anomalies and the topological Green-Schwarz mechanism

String theory provides us with 8d supersymmetric gauge theory with gauge algebras \( \mathfrak{s}\mathfrak{u}(N),\mathfrak{s}\mathfrak{o}(2N),\mathfrak{s}\mathfrak{p}(N),{\mathfrak{e}}_6,{\mathfrak{e}}_7\kern0.5em \mathrm{and}\kern0.5em {\mathfrak{e}}_8 \), but no construction for \( \mathfrak{so}\left(2N+1\right) \), \( {\mathfrak{f}}_4 \) and \( {\mathfrak{g}}_2 \) is known. In...

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.

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...

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...

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...

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 six...

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