# 4th "Strings in Greater Tokyo" meeting

April 12th, 2016

## Place

U. Tokyo, Hongo campus, Building 1 of Faculty of Science, Room 206

Map of the Campus with the building marked blue

## Registration

Not necessary. Please just show up!

## Timetable

 10:00 – 12:00 Yuji Okawa (Komaba) "The basics of open bosonic string field theory" (on blackboards) 13:30 – 14:30 Yuji Okawa (Komaba) "Complete action for open superstring field theory" 14:45 – 15:45 Edgar Shaghoulian (UCSB) "Modular forms, new Cardy formulas, and black hole entropy" (on blackboards) 16:00 – 17:30 Short talk session (30 min each) Tetsuji Kimura (Keio) "Exotic brane junctions from F-theory" Takaki Matsumoto (Tsukuba) "Kahler Structure in Matrix Geometry" Rui-Dong Zhu (Hongo) "Derivation of qq-characters within the framework of quantum W1+∞ algebra"

## Abstracts

Yuji Okawa (lecture): "The basics of open bosonic string field theory”
based on his review paper Prog. Theor. Phys. 128 (2012) 1001-1060
Yuji Okawa (seminar): "Complete action for open superstring field theory"
In formulating superstring field theory, construction of an action including the Ramond sector has not been successful for about thirty years, and this has been a major obstacle. Last year we finally succeeded in constructing a gauge-invariant action for open superstring field theory including both the Neveu-Schwarz sector and the Ramond sector. This is the first construction of a complete formulation of superstring field theory. In this talk, we explain the construction of the complete action without assuming any background on string field theory. The talk is based on the paper arXiv:1508.00366 in collaboration with Kunitomo.
Edgar Shaghoulian: "Modular forms, new Cardy formulas, and black hole entropy”
We will utilize modular invariance of (d+1)-dimensional conformal field theories to argue that the logarithm of the partition function transforms as the absolute value of a modular form of weight d-1. We will use this property to derive new Cardy formulas which relate the asymptotic degeneracy of states with fixed charges to the vacuum energy. After a few checks of the formulas, we will use them to reproduce the Bekenstein-Hawking entropy of large AdS-Schwarzschild black holes, including logarithmic corrections. This generalizes Strominger's microscopic count of the BTZ black hole entropy to higher dimensions.
Tetsuji Kimura: "Exotic brane junctions from F-theory"
Applying string dualities to F-theory, we obtain various [p,q]-branes whose constituents are standard branes of codimension two and exotic branes. We construct junctions of the exotic five-branes and their Hanany-Witten transitions associated with those in F-theory. In this procedure, we understand the monodromy of the single $5^2_2$-brane. We also find the objects which are sensitive to the branch cut of the $5^2_2$-brane. Considering the web of branes in the presence of multiple exotic five-branes analogous to the web of five-branes with multiple seven-branes, we obtain novel brane constructions for SU(2) gauge theories with n flavors and their superconformal limit with enhanced $E_{n+1}$ symmetry in five, four, and three dimensions. Hence, adapting the techniques of the seven-branes to the exotic branes, we will be able to construct F-theories in diverse dimensions. Based on arXiv:1602.08606
Takaki Matsumoto: "Kahler Structure in Matrix Geometry”
We consider a matrix geometry described by a large-N sequence of Hermitian matrices. We define a corresponding classical space as a set of coherent states, which are defined from given matrices. Then, we show that under some assumptions the classical space becomes a Kahler manifold. The Kahler structure on the classical space (i.e. Riemann structure, symplectic structure, and complex structure) is expressed in terms of the matrix elements. We also relate our construction to the geometric quantization. This talk is based on the collaboration with Ishiki-san and Muraki-san in University of Tsukuba.
Rui-Dong Zhu: "Derivation of qq-characters within the framework of quantum W1+∞ algebra"
A brief review on the 4d story will be given first. We use the so-called SH$^c$ algebra to reproduce the instanton part of the Nekrasov partition function for 4d N=2 quiver gauge theory. The qq-character can be obtained through the Ward identity in SH$^c$, which in the "classical" limit ($\epsilon_1, \epsilon_2\to 0$) reduces to the Seiberg-Witten curve and in general gives its quantized version. In the latter half of this talk, we generalize the idea to 5d N=1 quiver gauge theories (on $S^1$). The corresponding algebra is the q-deformed algebra of SH$^c$, quantum $W_{1+\infty}$ algebra. We will see again that the Ward identity gives rise to the Seiberg-Witten curve in the "classical" limit and we obtain the expression for qq-characters from the Ward identity. A few examples and comparison between these two cases will also be presented.

## Organizers

Tatsuma Nishioka, Itamar Yaakov, Yuji Tachikawa