47 research outputs found

### Large N duality beyond the genus expansion

We study non-perturbative aspects of the large N duality between Chern-Simons
theory and topological strings, and we find a rich structure of large N phase
transitions in the complex plane of the 't Hooft parameter. These transitions
are due to large N instanton effects, and they can be regarded as a deformation
of the Stokes phenomenon. Moreover, we show that, for generic values of the 't
Hooft coupling, instanton effects are not exponentially suppressed at large N
and they correct the genus expansion. This phenomenon was first discovered in
the context of matrix models, and we interpret it as a generalization of the
oscillatory asymptotics along anti-Stokes lines. In the string dual, the
instanton effects can be interpreted as corrections to the saddle string
geometry due to discretized neighboring geometries. As a mathematical
application, we obtain the 1/N asymptotics of the partition function of
Chern-Simons theory on L(2,1), and we test it numerically to high precision in
order to exhibit the importance of instanton effects.Comment: 37 pages, 24 figures. v2: clarifications and references added,
misprints corrected, to appear in JHE

### (0,2) Trialities

Motivated by the connection between 4-manifolds and 2d N=(0,2) theories, we
study the dynamics of a fairly large class of 2d N=(0,2) gauge theories. We see
that physics of such theories is very rich, much as the physics of 4d N=1
theories. We discover a new type of duality that is very reminiscent of the 4d
Seiberg duality. Surprisingly, the new 2d duality is an operation of order
three: it is IR equivalence of three different theories and, as such, is
actually a triality. We also consider quiver theories and study their triality
webs. Given a quiver graph, we find that supersymmetry is dynamically broken
unless the ranks of the gauge groups and flavor groups satisfy stringent
inequalities. In fact, for most of the graphs these inequalities have no
solutions. This supports the folklore theorem that generic 2d N=(0,2) theories
break supersymmetry dynamically.Comment: 31 pages, 12 figure

### $(0, 4)$ dualities

We study a class of two-dimensional ${\cal N}=(0, 4)$ quiver gauge theories
that flow to superconformal field theories. We find dualities for the
superconformal field theories similar to the 4d ${\cal N}=2$ theories of class
${\cal S}$, labelled by a Riemann surface ${\cal C}$. The dual descriptions
arise from various pair-of-pants decompositions, that involves an analog of the
$T_N$ theory. Especially, we find the superconformal index of such theories can
be written in terms of a topological field theory on ${\cal C}$. We interpret
this class of SCFTs as the ones coming from compactifying 6d ${\cal N}=(2, 0)$
theory on $\mathbb{CP}^1 \times {\cal C}$Comment: 41 pages, 12 figure

### Vertex algebras and 4-manifold invariants

We propose a way of computing 4-manifold invariants, old and new, as chiral
correlation functions in half-twisted 2d $\mathcal{N}=(0,2)$ theories that
arise from compactification of fivebranes. Such formulation gives a new
interpretation of some known statements about Seiberg-Witten invariants, such
as the basic class condition, and gives a prediction for structural properties
of the multi-monopole invariants and their non-abelian generalizations.Comment: 67 pages, 11 figure

### Resurgence in complex Chern-Simons theory

We study resurgence properties of partition function of SU(2) Chern-Simons
theory (WRT invariant) on closed three-manifolds. We check explicitly that in
various examples Borel transforms of asymptotic expansions posses expected
analytic properties. In examples that we study we observe that contribution of
irreducible flat connections to the path integral can be recovered from
asymptotic expansions around abelian flat connections. We also discuss
connection to Floer instanton moduli spaces, disk instantons in 2d sigma
models, and length spectra of "complex geodesics" on the A-polynomial curve.Comment: 56 pages, 19 figures. v2: references adde

### Spin-cobordisms, surgeries and fermionic modular bootstrap

We consider general fermionic quantum field theories with a global finite
group symmetry $G$, focusing on the case of 2-dimensions and torus spacetime.
The modular transformation properties of the family of partition functions with
different backgrounds is determined by the 't Hooft anomaly of $G$ and fermion
parity. For a general possibly non-abelian $G$ we provide a method to determine
the modular transformations directly from the bulk 3d invertible topological
quantum field theory (iTQFT) corresponding to the anomaly by inflow. We also
describe a method of evaluating the character map from the real representation
ring of $G$ to the group which classifies anomalies. Physically the value of
the map is given by the anomaly of free fermions in a given representation. We
assume classification of the anomalies/iTQFTs by spin-cobordisms. As a
byproduct, for all abelian symmetry groups $G$, we provide explicit
combinatorial expressions for corresponding spin-bordism invariants in terms of
surgery representation of arbitrary closed spin 3-manifolds. We work out the
case of $G=\mathbb{Z}_2$ in detail, and, as an application, we consider the
constraints that 't Hooft anomaly puts on the spectrum of the infrared
conformal field theory.Comment: 86 pages, 27 figure