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 study the interpretation of O7+-planes in F-theory, mainly in the context of the six-dimensional models. In particular, we study how to assign gauge algebras and matter content to seven-branes and their intersections, and the implication of anomaly cancellation in our construction, generalizing earlier analyses without any O7+-planes. By including O7+-planes we can realize 6d superconformal field theories hitherto unobtainable in F-theory, such as those with hypermultiplets in the symmetric representation of su. We also examine a couple of compact models. These reproduce some famous perturbative models, and in some cases enhance their gauge symmetries non-perturbatively.

/pdf/the-frozen-phase-of-f-theory-4msb0te4wx.pdf

The frozen phase of F-theory

We study 4D N=2 superconformal theories that arise from the compactification of 6D N=(2,0) theories of type A_{2N-1} on a Riemann surface C, in the presence of punctures twisted by a Z_2 outer automorphism. We describe how to do a complete classification of these SCFTs in terms of three-punctured spheres and cylinders, which we do explicitly for A_3, and provide tables of properties of twisted defects up through A_9. We find atypical degenerations of Riemann surfaces that do not lead to weakly-coupled gauge groups, but to a gauge coupling pinned at a point in the interior of moduli space. 
As applications, we study: i) 6D representations of 4D superconformal quivers in the shape of an affine/non-affine D_n Dynkin diagram, ii) S-duality of SU(4) and Sp(2) gauge theories with various combinations of fundamental and antisymmetric matter, and iii) realizations of all rank-one SCFTs predicted by Argyres and Wittig.

Gaiotto Duality for the Twisted A_{2N-1} Series

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.

/pdf/anomaly-of-strings-of-6d-mathcal-n-left-1-0-right-theories-40vopa18of.pdf

Anomaly of strings of 6d $ \mathcal{N}=\left(1,0\right) $ 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 central charges a and c in terms of l, and construct the associated 2d chiral algebras, which turn out to be exotic $$ \mathcal{N}=2 $$
 supersymmetric W-algebras.

/pdf/on-4d-rank-one-n-3-superconformal-field-theories-50fhfmjo59.pdf

On 4d rank-one N=3 superconformal field theories

Compactification of 6D theory of type G on a punctured Riemann surface has been effectively used to understand S-dualities of 4D theories. We can further introduce branch cuts on the Riemann surface across which the worldvolume fields are transformed by the discrete symmetries associated with those of the Dynkin diagram of type G. This allows us to generate more S-dualities, and in particular to reproduce a couple of S-dual pairs found previously by Argyres and Wittig.

Yuji Tachikawa

Papers

The frozen phase of F-theory

Gaiotto Duality for the Twisted A_{2N-1} Series

Anomaly of strings of 6d $ \mathcal{N}=\left(1,0\right) $ theories

On 4d rank-one N=3 superconformal field theories

N = 2 S-duality via outer-automorphism twists