55 research outputs found
Hanany-Witten effect and SL(2,Z) dualities in matrix models
We provide tests of dualities for three-dimensional N=4 quiver SCFTs with
brane realizations in IIB string theory, by matching their exact partition
functions on . The dualities are generated by SL(2,Z) transformations and
Hanany-Witten 5-brane moves. These contain mirror symmetry as well as dualities
identifiying fixed points of Yang-Mills quivers and Chern-Simons theories. The
partition function is given by a matrix model, that can be nicely rearranged
into a sequence of factors mimicking the brane realization. Identities obeyed
by these elementary factors can be used to match the partition functions of
dual theories, providing tests for the full web of dualities. In particular we
are able to check mirror symmetry for linear and circular quivers with gauge
nodes of arbitrary ranks. Our analysis also leads to a proof of a conjectured
formula evaluating the matrix models of linear quiver theories.Comment: 65 pages, 23 figures, v2, minor clarifications added, version
published on JHE
Mirror Symmetry And Loop Operators
Wilson loops in gauge theories pose a fundamental challenge for dualities.
Wilson loops are labeled by a representation of the gauge group and should map
under duality to loop operators labeled by the same data, yet generically, dual
theories have completely different gauge groups. In this paper we resolve this
conundrum for three dimensional mirror symmetry. We show that Wilson loops are
exchanged under mirror symmetry with Vortex loop operators, whose microscopic
definition in terms of a supersymmetric quantum mechanics coupled to the theory
encode in a non-trivial way a representation of the original gauge group,
despite that the gauge groups of mirror theories can be radically different.
Our predictions for the mirror map, which we derive guided by branes in string
theory, are confirmed by the computation of the exact expectation value of
Wilson and Vortex loop operators on the three-sphere.Comment: 92 pages, v2: minor clarifications in the introduction, to be
published in JHE
Six-dimensional Origin of SYM with Duality Defects
We study the topologically twisted compactification of the 6d
M5-brane theory on an elliptically fibered K\"ahler three-fold preserving two
supercharges. We show that upon reducing on the elliptic fiber, the 4d theory
is Super-Yang Mills, with varying complexified coupling ,
in the presence of defects. For abelian gauge group this agrees with the
so-called duality twisted theory, and we determine a non-abelian generalization
to . When the elliptic fibration is singular, the 4d theory contains 3d
walls (along the branch-cuts of ) and 2d surface defects, around which
the 4d theory undergoes duality transformations. Such
duality defects carry chiral fields, which from the 6d point of view arise as
modes of the two-form in the tensor multiplet. Each duality defect has a
flavor symmetry associated to it, which is encoded in the structure of the
singular elliptic fiber above the defect. Generically 2d surface defects will
intersect in points in 4d, where there is an enhanced flavor symmetry. The 6d
point of view provides a complete characterization of this 4d-3d-2d-0d
`Matroshka'-defect configuration.Comment: 62 pages, 4 figure
Partition functions of 3d -quivers and their mirror duals from 1d free fermions
We study the matrix models calculating the sphere partition functions of 3d
gauge theories with supersymmetry and a quiver structure of a
Dynkin diagram (where each node is a unitary gauge group). As in the
case of necklace () quivers, we can map the problem to that of free
fermion quantum mechanics whose complicated Hamiltonian we find explicitly.
Many of these theories are conjectured to be dual under mirror symmetry to
certain unitary linear quivers with extra Sp nodes or antisymmetric
hypermultiplets. We show that the free fermion formulations of such mirror
pairs are related by a linear symplectic transformation.
We then study the large N expansion of the partition function, which as in
the case of the -quivers is given to all orders in 1/N by an Airy
function. We simplify the algorithm to calculate the numerical coefficients
appearing in the Airy function and evaluate them for a wide class of -quiver theories.Comment: 39 pages, 8 figure
The Space of Vacua of 3d Abelian Theories
We use brane techniques to study the space of vacua of abelian 3d
gauge theories. The coordinates on these spaces are the vevs of
chiral monopole and meson operators, which are realized in the type IIB brane
configuration of the theory by adding semi-infinite strings or F1
strings. The study of various brane setups allows us to determine a basis of
chiral operators and chiral ring relations relevant to each branch of vacua,
leading to the algebraic description of these branches. The method is mostly
graphical and does not require actual computations. We apply it and provide
explicit results in various examples. For linear quivers we find that the space
of vacua has in general a collection of Coulomb-like branches, a Higgs branch
and mixed branches. For circular quivers we find an extra branch, the geometric
branch, parametrized by monopoles with equal magnetic charges in all
nodes and meson operators. We explain how to include FI and mass deformations.
We also study theories realized with 5-branes.Comment: 78 pages, 41 figure
Note on Monopole Operators in Chern-Simons-Matter Theories
Monopole operators in Chern-Simons theories with charged matter have been
studied using the state-operator map in CFTs, as states on with background magnetic flux on . Gauge invariance requires a
dressing with matter modes which provides non-zero spin to the monopoles. In
this note we propose a description of the monopole operators directly on
, as a singular behavior of the gauge and matter fields in the
vicinity of the insertion point, with a dressing. We study abelian theories
with a charged boson or a charged fermion. We extend the discussion to abelian
supersymmetric Chern-Simons-matter theories and describe the BPS monopoles,
which have spin and preserve a single supercharge. We match our results against
the prediction from the superconformal index.Comment: 34 pages. v2: Some clarification on Chern-Simons level quantization
in theories with fermions adde
M5-branes on S^2 x M_4: Nahm's Equations and 4d Topological Sigma-models
We study the 6d N=(0,2) superconformal field theory, which describes multiple
M5-branes, on the product space S^2 x M_4, and suggest a correspondence between
a 2d N=(0,2) half-twisted gauge theory on S^2 and a topological sigma-model on
the four-manifold M_4. To set up this correspondence, we determine in this
paper the dimensional reduction of the 6d N=(0,2) theory on a two-sphere and
derive that the four-dimensional theory is a sigma-model into the moduli space
of solutions to Nahm's equations, or equivalently the moduli space of
k-centered SU(2) monopoles, where k is the number of M5-branes. We proceed in
three steps: we reduce the 6d abelian theory to a 5d Super-Yang-Mills theory on
I x M_4, with I an interval, then non-abelianize the 5d theory and finally
reduce this to 4d. In the special case, when M_4 is a Hyper-Kahler manifold, we
show that the dimensional reduction gives rise to a topological sigma-model
based on tri-holomorphic maps. Deriving the theory on a general M_4 requires
knowledge of the metric of the target space. For k=2 the target space is the
Atiyah-Hitchin manifold and we twist the theory to obtain a topological
sigma-model, which has both scalar fields and self-dual two-forms.Comment: 78 pages, 2 figure
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