There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

To say that this is the best book on the quantum theory of fields is no praise, since to my knowledge it is the only book on this subject But it is a very good and most useful book The original was written in German and appeared in 1942 This is a translation with some minor changes A few remarks have been added, concerning meson theory and nuclear forces, also footnotes referring to modern work in this field, and finally an appendix on the symmetrization of the energy momentum tensor according to Belinfante Quantum Theory of Fields Prof Gregor Wentzel Translated from the German by Charlotte Houtermans and J M Jauch Pp ix + 224, (New York and London: Interscience Publishers, Inc, 1949) 36s

Quantum Theory of Fields

Superstring theoryをめぐって(放談室)

These notes are loosely based on lectures given at the CERN Winter School on Supergravity, Strings and Gauge theories, February 2009, and at the IPM String School in Tehran, April 2009. I have focused on a few concrete topics and also on addressing questions that have arisen repeatedly. Background condensed matter physics material is included as motivation and easy reference for the high energy physics community. The discussion of holographic techniques progresses from equilibrium, to transport and to superconductivity.

https://iopscience.iop.org/article/10.1088/0264-9381/26/22/224002/pdf

Lectures on holographic methods for condensed matter physics

We use the AdS/CFT correspondence to compute the central charges of the d=4, N=2 superconformal field theories arising from N D3-branes at singularities in F-theory. These include the conformal theories with E_n global symmetries. We compute the central charges a and c related to the conformal anomaly, and also the central charges k associated to the global symmetry in these theories. All of these are related to the coefficients of Chern-Simons terms in the dual string theory on AdS_5. Our computation is exact for all values of N, enabling several tests of the dualities recently proposed by Argyres and Seiberg for the E_6 and E_7 theories with N=1.

A holographic computation of the central charges of d=4, N=2 SCFTs

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 Garcia-Etxebarria and Regalado to provide the first construction of four dimensional N=3 superconformal theories. In this note, we classify the different variants of these N=3 preserving S-folds, distinguished by an analog of discrete torsion, using both a direct analysis of the different torsion classes and the compactification of the S-folds to three dimensional M-theory backgrounds. Upon adding D3-branes, these variants lead to different classes of N=3 superconformal field theories. We also analyze the holographic duals of these theories, and in particular clarify the role of discrete gauge and global symmetries in holography.

/pdf/s-folds-and-4d-n-3-superconformal-field-theories-2y4rip4huk.pdf

S-folds and 4d N=3 superconformal field 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 six-dimensional 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.

Instanton operators and symmetry enhancement in 5d supersymmetric gauge theories

We study a duality of 5d maximally supersymmetric Yang-Mills on S
 1, which exchanges the tower of Kaluza-Klein W-bosons and the tower of instantonic monopoles. This duality maps a non-simply-laced gauge theory to a simply-laced gauge theory twisted by an outer automorphism around S
 1, and is closely related to the Langlands dual of affine Lie algebras. We also discuss how this S-duality is implemented in terms of 6d $\mathcal{N}$
 = (2, 0) theory. This is straightforward except for the 6d theory of type SU(2n + 1) with ${\mathbb{Z}_2}$
 outer-automorphism twist, for which a few new properties are deduced. For example, this 6d theory, when reduced on an S
 1 with ${\mathbb{Z}_2}$
 twist, gives 5d USp(2n) theory with nontrivial discrete 5d theta angle.

On S-duality of 5d super Yang-Mills on S^1

We realize four-dimensional N=2 superconformal quiver gauge theories with alternating SO and USp gauge groups as compactifications of the six-dimensional D_N theory with defects. The construction can be used to analyze infinitely strongly-coupled limits and S-dualities of such gauge theories, resulting in a new class of isolated four-dimensional N=2 superconformal field theories with SO(2N)^3 flavor symmetry.

Yuji Tachikawa

Papers

A holographic computation of the central charges of d=4, N=2 SCFTs

S-folds and 4d N=3 superconformal field theories

Instanton operators and symmetry enhancement in 5d supersymmetric gauge theories

On S-duality of 5d super Yang-Mills on S^1

Six-dimensional D_N theory and four-dimensional SO-USp quivers