13,496 research outputs found
3d dualities from 4d dualities
Many examples of low-energy dualities have been found in supersymmetric gauge
theories with four supercharges, both in four and in three space-time
dimensions. In these dualities, two theories that are different at high
energies have the same low-energy limit. In this paper we clarify the relation
between the dualities in four and in three dimensions. We show that every four
dimensional duality gives rise to a three dimensional duality between theories
that are similar, but not identical, to the dimensional reductions of the four
dimensional dual gauge theories to three dimensions. From these specific three
dimensional dualities one can flow to many other low-energy dualities,
including known three dimensional dualities and many new ones. We discuss in
detail the case of three dimensional SU(N_c) supersymmetric QCD theories,
showing how to derive new duals for these theories from the four dimensional
duality.Comment: 84 pages, 3 figures, harvmac. v2: added an appendix on the reduction
of the 4d index to the 3d partition function, added references, minor
corrections and change
Chiral expansion and Macdonald deformation of two-dimensional Yang-Mills theory
We derive the analog of the large Gross-Taylor holomorphic string
expansion for the refinement of -deformed Yang-Mills theory on a
compact oriented Riemann surface. The derivation combines Schur-Weyl duality
for quantum groups with the Etingof-Kirillov theory of generalized quantum
characters which are related to Macdonald polynomials. In the unrefined limit
we reproduce the chiral expansion of -deformed Yang-Mills theory derived by
de Haro, Ramgoolam and Torrielli. In the classical limit , the expansion
defines a new -deformation of Hurwitz theory wherein the refined
partition function is a generating function for certain parameterized Euler
characters, which reduce in the unrefined limit to the orbifold Euler
characteristics of Hurwitz spaces of holomorphic maps. We discuss the
geometrical meaning of our expansions in relation to quantum spectral curves
and -ensembles of matrix models arising in refined topological string
theory.Comment: 45 pages; v2: References adde
Fundamental Vortices, Wall-Crossing, and Particle-Vortex Duality
We explore 1d vortex dynamics of 3d supersymmetric Yang-Mills theories, as
inferred from factorization of exact partition functions. Under Seiberg-like
dualities, the 3d partition function must remain invariant, yet it is not a
priori clear what should happen to the vortex dynamics. We observe that the 1d
quivers for the vortices remain the same, and the net effect of the 3d duality
map manifests as 1d Wall-Crossing phenomenon; Although the vortex number can
shift along such duality maps, the ranks of the 1d quiver theory are
unaffected, leading to a notion of fundamental vortices as basic building
blocks for topological sectors. For Aharony-type duality, in particular, where
one must supply extra chiral fields to couple with monopole operators on the
dual side, 1d wall-crossings of an infinite number of vortex quiver theories
are neatly and collectively encoded by 3d determinant of such extra chiral
fields. As such, 1d wall-crossing of the vortex theory encodes the
particle-vortex duality embedded in the 3d Seiberg-like duality. For , the D-brane picture is used to motivate this 3d/1d connection, while,
for , this 3d/1d connection is used to fine-tune otherwise
ambiguous vortex dynamics. We also prove some identities of 3d supersymmetric
partition functions for the Aharony duality using this vortex wall-crossing
interpretation.Comment: 75 pages, 24 figures; v2: a reference added, published versio
Guiding-center Hall viscosity and intrinsic dipole moment along edges of incompressible fractional quantum Hall fluids
The discontinuity of guiding-center Hall viscosity (a bulk property) at edges
of incompressible quantum Hall fluids is associated with the presence of an
intrinsic electric dipole moment on the edge. If there is a gradient of drift
velocity due to a non-uniform electric field, the discontinuity in the induced
stress is exactly balanced by the electric force on the dipole. The total Hall
viscosity has two distinct contributions: a "trivial" contribution associated
with the geometry of the Landau orbits, and a non-trivial contribution
associated with guiding-center correlations.
We describe a relation between the guiding-center edge-dipole moment and
"momentum polarization", which relates the guiding-center part of the bulk Hall
viscosity to the "orbital entanglement spectrum(OES)". We observe that using
the computationally-more-onerous "real-space entanglement spectrum (RES)" just
adds the trivial Landau-orbit contribution to the guiding-center part. This
shows that all the non-trivial information is completely contained in the OES,
which also exposes a fundamental topological quantity = , the difference between the "chiral stress-energy anomaly" (or signed
conformal anomaly) and the chiral charge anomaly. This quantity characterizes
correlated fractional quantum Hall fluids, and vanishes in uncorrelated integer
quantum Hall fluids
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