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 derive the general anomaly polynomial for a class of two-dimensional CFTs arising as twisted compactifications of a higher-dimensional theory on compact manifolds $\mathcal{M}_d$, including the contribution of the isometries of $\mathcal{M}_d$. We then use the result to perform a counting of microstates for electrically charged and rotating supersymmetric black strings in AdS$_5\times S^5$ and AdS$_7\times S^4$ with horizon topology BTZ$ \ltimes S^2$ and BTZ$ \ltimes S^2 \times \Sigma_\mathfrak{g}$, respectively, where $\Sigma_\mathfrak{g}$ is a Riemann surface. We explicitly construct the latter class of solutions by uplifting a class of four-dimensional rotating black holes. We provide a microscopic explanation of the entropy of such black holes by using a charged version of the Cardy formula.

/pdf/anomalies-black-strings-and-the-charged-cardy-formula-4uyyg614l0.pdf

Anomalies, Black strings and the charged Cardy formula.

Studying the supersymmetry enhancement mechanism of Aharony, Bergman, Jafferis and Maldacena, we find a simple condition on the gauge group generators for the matter fields. We analyze all possible compact Lie groups and their representations. The only allowed gauge groups leading to the manifest [FORMULA] supersymmetry are, up to discrete quotients, SU(n) ×U(1), Sp(n) ×U(1), SU(n) ×SU(n), and SU(n) ×SU(m) ×U(1) with possibly additional U(1)’s. Matter representations are restricted to be the (bi)fundamentals. As a byproduct we obtain another proof of the complete classification of the three algebras considered by Bagger and Lambert.

Classification of [FORMULA] superconformal theories of ABJM type

In the last few years it was realized that every fermionic theory in 1+1 dimensions is a generalized Jordan-Wigner transform of a bosonic theory with a non-anomalous $\mathbb{Z}_2$ symmetry. In this note we determine how the boundary states are mapped under this correspondence. We also interpret this mapping as the fusion of the original boundary with the fermionization interface.

/pdf/fermionization-and-boundary-states-in-1-1-dimensions-534pwltv1q.pdf

Fermionization and boundary states in 1+1 dimensions

In the past few years we saw significant advancement in understanding the strong-weak duality of = 2 supersymmetric theories in four dimensions, initiated by the seminal works by Argyres and Seiberg [1], and then greatly generalized by Gaiotto [2]. A most surprising feature of this new duality is that the dual of a normal supersymmetric gauge theory can involve a strange mixture of weakly-coupled gauge multiplets and non-Lagrangian superconformal field theories. Here we illustrate these new dualities by reviewing known examples and then by demonstrating new dual pairs. This work is based on the author's collaboration with Benini and Benvenuti [3].

Some illustrative examples of Argyres-Seiberg-Gaiotto duality

It is well-known that the value of the Frobenius–Schur indicator $$|G|^{-1} \sum _{g\in G} \chi (g^2)=\pm 1$$ of a real irreducible representation of a finite group G determines which of the two types of real representations it belongs to, i.e. whether it is strictly real or quaternionic. We study the extension to the case when a homomorphism $$\varphi :G\rightarrow \mathbb {Z}/2\mathbb {Z}$$ gives the group algebra $$\mathbb {C}[G]$$ the structure of a superalgebra. Namely, we construct of a super version of the Frobenius–Schur indicator whose value for a real irreducible super representation is an eighth root of unity, distinguishing which of the eight types of irreducible real super representations described in Wall (in J Reine Angew Math 213:187–199, 1963/64. https://doi.org/10.1515/crll.1964.213.187 ) it belongs to. We also discuss its significance in the context of two-dimensional finite-group gauge theories on pin $$^-$$ surfaces. 

/pdf/the-super-frobenius-schur-indicator-and-finite-group-gauge-2ye1gq6d.pdf

Yuji Tachikawa

Papers

Anomalies, Black strings and the charged Cardy formula.

Classification of [FORMULA] superconformal theories of ABJM type

Fermionization and boundary states in 1+1 dimensions

Some illustrative examples of Argyres-Seiberg-Gaiotto duality

The Super Frobenius–Schur Indicator and Finite Group Gauge Theories on Pin$$^-$$ Surfaces