179 research outputs found

### Macdonald Index and Chiral Algebra

For any 4d N=2 SCFT, there is a subsector described by a 2d chiral algebra.
The vacuum character of the chiral algebra reproduces the Schur index of the
corresponding 4d theory. The Macdonald index counts the same set of operators
as the Schur index, but the former has one more fugacity than the latter. We
conjecture a prescription to obtain the Macdonald index from the chiral
algebra. The vacuum module admits a filtration, from which we construct an
associated graded vector space. From this grading, we conjecture a notion of
refined character for the vacuum module of a chiral algebra, which reproduces
the Macdonald index. We test this prescription for the Argyres-Douglas theories
of type $(A_1, A_{2n})$ and $(A_1, D_{2n+1})$ where the chiral algebras are
given by Virasoro and su(2) affine Kac-Moody algebra. When the chiral algebra
has more than one family of generators, our prescription requires a knowledge
of the generators from the 4d.Comment: 25 pages, v2: major revision. Clarified the prescription to get the
Macdonald grading; v3: corrected hyperlinks to the references. To appear in
JHE

### N=1 Deformations and RG Flows of N=2 SCFTs

We study certain N=1 preserving deformations of four-dimensional N=2
superconformal field theories (SCFTs) with non-abelian flavor symmetry. The
deformation is described by adding an N=1 chiral multiplet transforming in the
adjoint representation of the flavor symmetry with a superpotential coupling,
and giving a nilpotent vacuum expectation value to the chiral multiplet which
breaks the flavor symmetry. This triggers a renormalization group flow to an
infrared SCFT. Remarkably, we find classes of theories flow to enhanced N=2
supersymmetric fixed points in the infrared under the deformation. They include
generalized Argyres-Douglas theories and rank-one SCFTs with non-abelian flavor
symmetries. Most notably, we find renormalization group flows from the deformed
conformal SQCDs to the $(A_1, A_n)$ Argyres-Douglas theories. From these
"Lagrangian descriptions," we compute the full superconformal indices of the
$(A_1, A_n)$ theories and find agreements with the previous results.
Furthermore, we study the cases, including the $T_N$ and $R_{0,N}$ theories of
class $\mathcal{S}$ and some of rank-one SCFTs, where the deformation gives
genuine N=1 fixed points.Comment: 45 pages, v2: added a paragraph on SUSY enhancement from the index.
Minor corrections. To appear in JHE

### New N=1 Dualities from M5-branes and Outer-automorphism Twists

We generalize recent construction of four-dimensional $\mathcal{N}=1$ SCFT
from wrapping six-dimensional $\mathcal{N}=(2,0)$ theory on a Riemann surface
to the case of $D$-type with outer-automorphism twists. This construction
allows us to build various dual theories for a class of $\mathcal{N}=1$ quiver
theories of $SO-USp$ type. In particular, we find there are five dual frames to
$SO(2N)/USp(2N-2)/G_2$ gauge theories with $(4N-4)/4N/8$ fundamental flavors,
where three of them are non-Lagrangian. We check the dualities by computing the
anomaly coefficients and the superconformal indices. In the process we verify
that the index of $D_4$ theory on a certain three punctured sphere with $Z_2$
and $Z_3$ twist lines exhibits the expected symmetry enhancement from $G_2
\times USp(6)$ to $E_7$.Comment: 56 pages, 29 colored figures; v2: minor corrections, references adde

### Four-dimensional Lens Space Index from Two-dimensional Chiral Algebra

We study the supersymmetric partition function on $S^1 \times L(r, 1)$, or
the lens space index of four-dimensional $\mathcal{N}=2$ superconformal field
theories and their connection to two-dimensional chiral algebras. We primarily
focus on free theories as well as Argyres-Douglas theories of type $(A_1, A_k)$
and $(A_1, D_k)$. We observe that in specific limits, the lens space index is
reproduced in terms of the (refined) character of an appropriately twisted
module of the associated two-dimensional chiral algebra or a generalized vertex
operator algebra. The particular twisted module is determined by the choice of
discrete holonomies for the flavor symmetry in four-dimensions.Comment: 47 pages; v2: minor corrections, published versio

### The Seiberg-Witten Kahler Potential as a Two-Sphere Partition Function

Recently it has been shown that the two-sphere partition function of a gauged
linear sigma model of a Calabi-Yau manifold yields the exact quantum Kahler
potential of the Kahler moduli space of that manifold. Since four-dimensional
N=2 gauge theories can be engineered by non-compact Calabi-Yau threefolds, this
implies that it is possible to obtain exact gauge theory Kahler potentials from
two-sphere partition functions. In this paper, we demonstrate that the
Seiberg-Witten Kahler potential can indeed be obtained as a two-sphere
partition function. To be precise, we extract the quantum Kahler metric of 4D
N=2 SU(2) Super-Yang-Mills theory by taking the field theory limit of the
Kahler parameters of the O(-2,-2) bundle over P1 x P1. We expect this method of
computing the Kahler potential to generalize to other four-dimensional N=2
gauge theories that can be geometrically engineered by toric Calabi-Yau
threefolds.Comment: 12 pages + appendix; v2: minor corrections, reference adde

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