March 27 (Mon)
9:50 — 10:00 Opening Remarks
10:00 — 11:00 Sungjay Lee (KIAS)
Title: On Classification of Fermionic Rational CFT
Abstract:
We systematically study how the integrality of the conformal characters shapes the space of fermionic rational conformal field theories in two dimensions. The integrality suggests that conformal characters on torus with a given choice of spin structures should be invariant under a principal congruence subgroup of PSL(2,Z). The invariance strongly constrains the possible values of the central charge as well as the conformal weights in both Neveu-Schwarz and Ramond sectors, which improves the conventional holomorphic modular bootstrap method in a significant manner. This allows us to make much progress on the classification of fermionic rational conformal field theories with the number of independent characters less than five.
11:30 — 12:30 Yosuke Imamura (Tokyo Institute of Technology)
Title: Invertible giant graviton expansions
Abstract:
We study some examples of giant graviton expansions of the superconformal index (SCI). In particular, we focus on the expansions with simple sum. In general, the simple-sum giant graviton expansion expresses the SCI of a theory A[N] with rank N as a series of the SCI of another set of theories B[m] with rank m. We find that this relation is invertible, meaning that the SCI of B[m] can also be expressed as a series of the SCI of A[N].
14:00 — 15:00 Hiroaki Kanno (Nagoya U.)
Title: K theoretic instanton counting with a defect and qq-Painlevé VI equation
Abstract:
We argue that the non-stationary difference equation proposed by S.Shikirov [arXiv 2111.07939] is identified with a quantization of the discrete version of Painlev\’e VI equation, whose time evolution is generated by a translation element in the extended affine Well group of D_5^{(1)}. Accordingly, the original difference equation can be factorized into a coupled system. We conjecture that solutions to the coupled system are given by the instanton partition function of the five dimensional SU(2) gauge theory with a surface defect. The talk is based on a collaboration with H.Awata, K.Hasegawa, R.Ohkawa, S.Shakirov, J.Shiraishi and Y.Yamada, arXiv [2211.16772].
15:30 — 16:00 Masashi Hamanaka (Nagoya U.)
Title: Solitons in 4-dim. WZW Model
Abstract:
Four-dimensional Wess-Zumino-Witten (WZW_4) models are analogous to the two dimensional WZW models. Equation of motion of the WZW_4 model is the Yang equation which is equivalent to the anti-self-dual Yang-Mills equation. In the split signature (+,+,-,-), the WZW_4 model describes the open N=2 string theory in the four-dimensional space-time. In this talk, we discuss soliton-type classical solutions of the WZW_4 model (mainly in the split signature) by calculating the action density of the WZW_4 model. We find that the action density of the one-soliton solutions is localized on a three-dimensional hyperplane. This shows that there would be codimension-one-solitonic objects, or equivalently, some kind of three-branes in the open N=2 string theory. We also prove that in the asymptotic region of the space-time, the action density of the n-soliton solutions is a ``nonlinear superposition'' of n one-solitons. This suggests the existence of intersecting n three-branes in the N=2 strings. Finally we make a reduction to (1+2)-dimensional real spaces to calculate energy densities of the soliton solutions. We can successfully evaluate the energy distribution for the two-soliton solutions and find that there is no singularity in the interacting region. This implies the existence of smooth intersecting codimension-one branes in the whole region. Soliton solutions and instanton solutions in the Euclidean signature are also discussed if time permits.
This talk is partially based on the collaboration with Shan-Chi Huang and Hiroaki Kanno (Nagoya): ``Solitons in Open N=2 String Theory,'' Progress of Theoretical and Experimental Physics (accepted) [arXiv:2212.11800]
16:00 — 16:30 Ryo Suzuki (Shing-Tung Yau Center of Southeast University)
Title: Tensionless limit of AdS3/CFT2 from integrability
Abstract:
The AdS3 x S3 x T4 spacetime with pure Ramond-Ramond flux, related to the D1-D5 system, is believed to be integrable as in AdS5 x S5. The integrability approaches to AdS3/CFT2 and the mirror TBA equations to study the energy spectrum are reviewed. By solving the TBA for massless excited states at small coupling, we find that the leading-order contribution to the anomalous dimensions includes massless wrapping corrections. This talk is based on arXiv:2303.02120 with Alberto Brollo, Dennis le Plat and Alessandro Sfondrini.
17:00 — 17:30 Sota Nakajima (KEK)
Title: New non-supersymmetric heterotic string theory with reduced rank and exponential suppression of the cosmological constant
Abstract:
We study the heterotic asymmetric orbifold model in which supersymmetry is broken by the stringy Schark-Schwarz mechanism. This model is a natural non-supersymmetric extension of CHL strings and can also be interpreted as the interpolating model between the $E_8 \times E_8$ theory and the non-supersymmetric $E_8$ theory. The enhancement of gauge groups, of which the rank is reduced to $8+d$, is explored. In particular, the enhancement to non-simply-laced groups is possible with $d \geq 2$, as well as in the CHL model. We also give the conditions that the massless matter spectrum must satisfy. Moreover, the one-loop cosmological constant is evaluated in the regime where supersymmetry is asymptotically restored, and we show that the exponential suppression can occur unless $d=1$.
March 28 (Tue)
10:00 — 11:00 Kimyeong Lee (KIAS)
Title: Twisting 6d SCFTs and LSTs
Abstract:
11:30 — 12:30 Mykola Dedushenko (SCGP, Stony Brook U.)
Title: Vertex algebra extensions and SQFT on the interval
Abstract:
Boundary conditions B preserving (0,2) supersymmetry in three-dimensional N=2 supersymmetric QFT (SQFT) support boundary vertex algebras VA[B]. When a theory is put on an interval, the N=(0,2) boundary conditions B_1 and B_2 support the boundary chiral algebras VA[B_1] and VA[B_2], and the total chiral algebra is a VOA obtained by extending VA[B_1] \otimes VA[B_2] by their bimodules. The latter correspond to SUSY line operators extended between the boundaries. I will discuss an example of this construction related to chiral differential operators on the group, with some puzzles and applications. Based on joint papers: one with M. Litvinov, and one with M. Litvinov and S. Alekseev.
14:00 — 15:00 Tomoyuki Arakawa (RIMS)
Title: On localization of Higgs branch VOAs
Abstract:
15:30 — 16:00 Shun Furihata (RIMS)
Title: On the Beem-Nair Conjecture
Abstract:
Given a simple Lie group G, we have an open immersion (constructed by Beem and Nair) from the Kostant-Toda lattice associated to G into the universal centralizer of G. They expected that a free field realization of the chiral universal centralizer of G at the critical level will be obtained by the chiralization of this immersion. In this talk, we will verify this conjecture is true by constructing an embedding from the chiral universal centralizer into an appropriate vertex operator algebra at any level.
16:00 — 16:30 Kaiwen Sun (KIAS)
Title: On intermediate Lie algebra $E_{7\frac12}$
Abstract:
$E_{7\frac12}$ is an intermediate Lie algebra filling the hole between $E_7$ and $E_8$ in the Deligne exceptional series. It was found independently by Mathur, Muhki, Sen in the modular bootstrap of 2d rational CFTs and by Deligne, Cohen, de Man in representation theory. We propose the VOA associated with $E_{7\frac12}$ at level 2 and the VOA associated with 4d rank-two instanton SCFT of $E_{7\frac12}$. We compute their characters and provide some coset constructions. These generalize the previous works of Kawasetsu for $E_{7\frac12}$ at level 1 and of Arakawa-Kawasetsu at level -5. This is based on a joint work with Kimyeong Lee and Haowu Wang.
17:00 — 17:30 Tomoki Nakanishi (Osaka Metropolitan U.)
Title: S^1 Reduction of 4D N=3 SCFTs and Squahing Independence of ABJM Theories
Abstract:
We study the compactification of 4D $¥mathcal{N}=3$ superconformal field theories (SCFTs) on $S^1$, focusing on the relation between the 4D superconformal index and 3D partition function on the squashed sphere $S^3_b$. Since the center $¥mathfrak{u}(1)$ of the $¥mathfrak{u}(3)$ R-symmetry of the 4D theory can mix with an $¥mathcal{N}=6$ abelian flavor symmetry in three dimensions, the precise 4D/3D relation for the global symmetry is not obvious. Focusing on the case in which the 3D theory is the ABJM theory we demonstrate that the above R-symmetry mixing can be precisely identified by considering the Schur limit (and/or its $¥mathcal{N}=3$ cousin) of the 4D index. As a result, we generalize to the ABJM theories recent discussions on the connection between supersymmetry enhancement of the 4D index and squashing independence of the $S^3_b$ partition function.
March 29 (Wed)
10:00 — 11:00 Yutaka Yoshida (Meiji Gaukuin U.)
Title: 3d Seiberg-like duality and quantum K-theory
Abstract:
In this talk, I will discuss the properties of quantum K-theory of the moduli space of the Higgs branch vacua predicted by the Seiberg-like duality of the Chern-Simons-matter theories. When two varieties are realized as the moduli spaces of a Seiberg-like dual pair, the K-theoretic I-functions with the level structure of these varieties satisfy a relation derived from the wall-crossing formula of indices of handsaw quiver varieties.
11:30 — 12:30 Hiraku Nakajima (Kavli IPMU)
Title: Coulomb branches and DAHA
Abstract:
I will review a mathematical approach to Coulomb branches of 3d N=4 theory in my joint work with Braverman and Finkelberg. Then I will explain DAHA as an example of a quantization of Coulomb branch. If time permits, I would like to explain one new example.
14:00 — 15:00 Piljin Yi (KIAS)
Title: On Holonomy Saddles
Abstract:
I overview the holonomy saddle and explore a few classes of theories where the notion offers crucial tools and cautionary tales when gauge theories are defined in spacetimes with nontrivial topology. Discussion will include (de)confinement transition, refined Witten indices, A-twisted susy partition functions, and 4d/5d relation of Seiberg-Witten theories. For the last example, we also give reconstruction of 5d BPS quivers via the holonomy saddles.
15:30 — 16:00 Mohammad Akhond (Kyoto U.)
Title: Higgs branch of Dp-O(p+2)^+ brane systems
Abstract:
16:00 — 16:30 Yongchao Lu (KIAS)
Title: Crystallographic complex reflection groups, 4d N=2 SCFTs, and Seiberg-Witten integrability
Abstract:
We study various classes of 4d N=2 SCFTs associated with crystallographic complex reflection groups (CCRG). We propose that the geometry of their Coulomb branch is captured by elliptic integrable systems of the Calogero-Moser type attached to CCRG. Using elliptic Cherednick algebra and elliptic Dunkl operators, we can derive the Lax matrix, spectral curve, and their quantizations. This talk will center on Mininan-Nemeschansky theories and their higher-rank generalizations, as well as their connection with Hitchin systems through class S construction and 5d quantum curves via circle compactification.
17:00 — 17:30 Reiji Yoshioka (OCAMI)
Title: Root of unity limit and elliptic deformation of q-Virasoro block
Abstract:
In the so-called AGT correspondence, the key object on the CFT side is the Virasoro (conformal) block. The q-Virasoro block is its q-analog, and it is known that the corresponding object is the 5-dimensional instanton partition function. In this talk, the root of unity limit and the elliptic deformation of q-Virasoro block will be discussed. The purpose of this talk is to provide an explicit formulation of these. I will show that the super Virasoro algebra appears in the root of unity limit, on the other hand the elliptic Virasoro block can be interpreted as a q-Virasoro block at finite temperature.
March 30 (Thu)
10:00 — 11:00 Kazunobu Maruyoshi (Seikei U.)
Title: Duality of adjoint SQCD with Argyres-Douglas blocks
Abstract:
11:30 — 12:30 Sanefumi Moriyama (Osaka Metropolitan U.)
Title: M2-branes —Parallelotopes and Bilinear Relations—
Abstract:
M2-branes are closely related to duality cascades. From physical questions on the finiteness and the uniqueness of duality cascades, we propose that the fundamental domain of duality cascades is a parallelotope, which is a polytope tiling the whole space by translations. For the special case with symmetries of the Weyl group, the parallelotope is the affine Weyl chamber enjoying hidden symmetries of the affine Weyl group. This implies that physical quantities of the system satisfy the q-Painleve equation. I will explain these aspects of M2-branes in my talk.
14:00 — 16:30 Free Discussions