Yuji Tachikawa

We study in general spacetime dimension the symmetry of the theory obtained by gauging a non-anomalous finite normal Abelian subgroup A <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>A</mml:mi> </mml:math> of a \Gamma <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>Γ</mml:mi> </mml:math> -symmetric theory. Depending on how anomalous \Gamma <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>Γ</m

We study the local properties of a class of codimension-2 defects of the 6d [Formula: see text] theories of type J = A, D, E labeled by nilpotent orbits of a Lie algebra [Formula: see text], where [Formula: see text] is determined by J and the outer-automorphism twist around the defect. This class is a natural generalization of the defects of the six-dimensional (6d) theory of type SU (N) labeled by a Young diagram with N boxes. For any of these defects, we determine its contribution to the dime

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 $$ \mathcal{N} $$ =3-preserving S-folds, distinguished by an analog of discrete torsion, using both a direct analys

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 around one-instanton operators.

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. Our analysis strongly suggests that the O7+ plane is the only completely frozen F-theory singularity.

Orientifold p <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>p</mml:mi> </mml:math> -planes with p\le 4 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>p</mml:mi> <mml:mo>≤</mml:mo> <mml:mn>4</mml:mn> </mml:mrow> </mml:math> have fractional D p <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>p</mml:mi> </mml:math> -charges, and therefore appear inconsistent with Dirac quantization

We describe a method to find the anomaly of the time-reversal symmetry of 2+1d topological quantum field theories, by computing the fractional anomalous momentum on the cross-cap background. This allows us, for example, to identify the parameter $\nu$ mod 16 of the bulk 3+1d topological superconductor with $\mathsf{T}^2=(-1)^F$ on whose boundary a given 2+1d time-reversal-invariant topological phase can appear.

A self-duality group $\cal G$ in quantum field theory can have anomalies. In that case, the space of ordinary coupling constants $\cal M$ can be extended to include the space $\cal F$ of coefficients of counterterms in background fields. The extended space $\cal N$ forms a bundle over $\cal M$ with fiber $\cal F$, and the topology of the bundle is determined by the anomaly. For example, the ${\cal G}=SL(2,\mathbb{Z})$ duality of the 4d Maxwell theory has an anomaly, and the space ${\cal F}=S^1$

We give a pedagogical introduction to the dynamics of N=2 supersymmetric systems in four dimensions. The topic ranges from the Lagrangian and the Seiberg-Witten solutions of SU(2) gauge theories to Argyres-Douglas CFTs and Gaiotto dualities. This is a write-up of the author's lectures at Tohoku University, Nagoya University and Rikkyo University. Comments will be appreciated.