58 research outputs found

### On the chiral algebra of Argyres-Douglas theories and S-duality

We study the two-dimensional chiral algebra associated with the simplest
Argyres-Douglas type theory with an exactly marginal coupling, i.e., the
$(A_3,A_3)$ theory. Near a cusp in the space of the exactly marginal
deformations (i.e., the conformal manifold), the theory is well-described by
the $SU(2)$ gauge theory coupled to isolated Argyres-Douglas theories and a
fundamental hypermultiplet. In this sense, the $(A_3,A_3)$ theory is an
Argyres-Douglas version of the $\mathcal{N}=2$ $SU(2)$ conformal QCD. By
studying its Higgs branch and Schur index, we identify the minimal possible set
of chiral algebra generators for the $(A_3,A_3)$ theory, and show that there is
a unique set of closed OPEs among these generators. The resulting OPEs are
consistent with the Schur index, Higgs branch chiral ring relations, and the
BRST cohomology conjecture. We then show that the automorphism group of the
chiral algebra we constructed contains a discrete group $G$ with an $S_3$
subgroup and a homomorphism $G\to S_4 \times {\bf Z}_2$. This result is
consistent with the S-duality of the $(A_3,A_3)$ theory.Comment: 25 pages, 2 figure

### OPE Selection Rules for Schur Multiplets in 4D $\mathcal{N}=2$ Superconformal Field Theories

We compute general expressions for two types of three-point functions of
(semi-)short multiplets in four-dimensional $\mathcal{N}=2$ superconformal
field theories. These (semi-)short multiplets are called "Schur multiplets" and
play an important role in the study of associated chiral algebras. The first
type of the three-point functions we compute involves two half-BPS Schur
multiplets and an arbitrary Schur multiplet, while the second type involves one
stress tensor multiplet and two arbitrary Schur multiplets. From these
three-point functions, we read off the corresponding OPE selection rules for
the Schur multiplets. Our results particularly imply that there are non-trivial
selection rules on the quantum numbers of Schur operators in these multiplets.
We also give a conjecture on the selection rules for general Schur multiplets.Comment: 39 page

### Two-dimensional crystal melting and D4-D2-D0 on toric Calabi-Yau singularities

We construct a two-dimensional crystal melting model which reproduces the BPS
index of D2-D0 states bound to a non-compact D4-brane on an arbitrary toric
Calabi-Yau singularity. The crystalline structure depends on the toric divisor
wrapped by the D4-brane. The molten crystals are in one-to-one correspondence
with the torus fixed points of the moduli space of the quiver gauge theory on
D-branes. The F- and D-term constraints of the gauge theory are regarded as a
generalization of the ADHM constraints on instantons. We also show in several
examples that our model is consistent with the wall-crossing formula for the
BPS index.Comment: 72 pages, 44 figure

### Topological strings and 5d T_N partition functions

We evaluate the Nekrasov partition function of 5d gauge theories engineered
by webs of 5-branes, using the refined topological vertex on the dual
Calabi-Yau threefolds. The theories include certain non-Lagrangian theories
such as the T_N theory. The refined topological vertex computation generically
contains contributions from decoupled M2-branes which are not charged under the
5d gauge symmetry engineered. We argue that, after eliminating them, the
refined topological string partition function agrees with the 5d Nekrasov
partition function. We explicitly check this for the T_3 theory as well as
Sp(1) gauge theories with N_f = 2, 3, 4 flavors. In particular, our method
leads to a new expression of the Sp(1) Nekrasov partition functions without any
contour integrals. We also develop prescriptions to calculate the partition
functions of theories obtained by Higgsing the T_N theory. We compute the
partition function of the E_7 theory via this prescription, and find the E_7
global symmetry enhancement. We finally discuss a potential application of the
refined topological vertex to non-toric web diagrams.Comment: 79 pages, 27 figures; v2: minor improvements, references adde

- β¦