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 point out that the choice of phases in Gliozzi-Scherk-Olive projections can be accounted for by a choice of fermionic symmetry-protected topological phases on the world sheet of the string. This point of view not only easily explains why there are essentially two type II theories, but also predicts that there are unoriented type 0 theories labeled by $n$ mod 8 and that there is an essentially unique choice of the type I world sheet theory. We also discuss the relationship between this point of view and the $K$-theoretic classification of D-branes.

Classification of String Theories via Topological Phases.

We study the Coulomb phase of N=1 SU(2)^3 gauge theory coupled to one trifundamental field, and generalizations thereof. The moduli space of vacua is always one-dimensional with multiple unbroken U(1) fields. We find that the N=1 Seiberg-Witten curve which encodes the U(1) couplings is given by the double cover of a Riemann surface branched at the poles and the zeros of a meromorphic function.

N=1 curves for trifundamentals

We argue that 6d N=(2,0) theory on S^1 x S^3 x C_2 reduces to the 2d q-deformed Yang-Mills on C_2 at finite area, as a small extension to the result of Gadde, Rastelli, Razamat and Yan. This is done by computing the partition function on S^1 x S^3 of 4d N=2 supersymmetric non-linear sigma model on T^*G_C, which gives the propagator of the 2d Yang-Mills.

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

We study how the charges of the black rings measured at the asymptotic infinity are encoded in the near-horizon metric and gauge potentials, independent of the detailed structure of the connecting region. Our analysis clarifies how different sets of four-dimensional charges can be assigned to a single five-dimensional object under the Kaluza-Klein reduction. Possible choices are related by the Witten effect on dyons and by the large gauge transformation in four and five dimensions, respectively.

Comments on Charges and Near-Horizon Data of Black Rings

https://link.springer.com/content/pdf/10.1007/JHEP03(2023)094.pdf

Yuji Tachikawa

Papers

Classification of String Theories via Topological Phases.

N=1 curves for trifundamentals

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

Comments on Charges and Near-Horizon Data of Black Rings

Asymptotic density of states in 2d CFTs with non-invertible symmetries