26 research outputs found
A note on the integral equation for the Wilson loop in N = 2 D=4 superconformal Yang-Mills theory
We propose an alternative method to study the saddle point equation in the
strong coupling limit for the Wilson loop in D=4 super
Yang-Mills with an SU(N) gauge group and 2N hypermultiplets. This method is
based on an approximation of the integral equation kernel which allows to solve
the simplified problem exactly. To determine the accuracy of this
approximation, we compare our results to those obtained recently by Passerini
and Zarembo. Although less precise, this simpler approach provides an explicit
expression for the density of eigenvalues that is used to derive the planar
free energy.Comment: 12 pages, v2: section 2.5 (Free Energy) amended and reference added,
to appear in J. Phys.
Loop operators and S-duality from curves on Riemann surfaces
We study Wilson-'t Hooft loop operators in a class of N=2 superconformal
field theories recently introduced by Gaiotto. In the case that the gauge group
is a product of SU(2) groups, we classify all possible loop operators in terms
of their electric and magnetic charges subject to the Dirac quantization
condition. We then show that this precisely matches Dehn's classification of
homotopy classes of non-self-intersecting curves on an associated Riemann
surface--the same surface which characterizes the gauge theory. Our analysis
provides an explicit prediction for the action of S-duality on loop operators
in these theories which we check against the known duality transformation in
several examples.Comment: 41 page
Exact Results in D=2 Supersymmetric Gauge Theories
We compute exactly the partition function of two dimensional N=(2,2) gauge
theories on S^2 and show that it admits two dual descriptions: either as an
integral over the Coulomb branch or as a sum over vortex and anti-vortex
excitations on the Higgs branches of the theory. We further demonstrate that
correlation functions in two dimensional Liouville/Toda CFT compute the S^2
partition function for a class of N=(2,2) gauge theories, thereby uncovering
novel modular properties in two dimensional gauge theories. Some of these gauge
theories flow in the infrared to Calabi-Yau sigma models - such as the conifold
- and the topology changing flop transition is realized as crossing symmetry in
Liouville/Toda CFT. Evidence for Seiberg duality in two dimensions is exhibited
by demonstrating that the partition function of conjectured Seiberg dual pairs
are the same.Comment: 78 pages, LaTeX; v2: small corrections and references added; v3: JHEP
version, discussing factorization further in new appendix F; v4: sign
corrected for non simply-connected gauge grou
A maximally supersymmetric Kondo model
We study the maximally supersymmetric Kondo model obtained by adding a
fermionic impurity to N=4 supersymmetric Yang-Mills theory. While the original
Kondo problem describes a defect interacting with a free Fermi liquid of
itinerant electrons, here the ambient theory is an interacting CFT, and this
introduces qualitatively new features into the system. The model arises in
string theory by considering the intersection of a stack of M D5-branes with a
stack of N D3-branes, at a point in the D3 worldvolume. We analyze the theory
holographically, and propose a dictionary between the Kondo problem and
antisymmetric Wilson loops in N=4 SYM. We perform an explicit calculation of
the D5 fluctuations in the D3 geometry and determine the spectrum of defect
operators. This establishes the stability of the Kondo fixed point together
with its basic thermodynamic properties. Known supergravity solutions for
Wilson loops allow us to go beyond the probe approximation: the D5s disappear
and are replaced by three-form flux piercing a new topologically non-trivial
three-sphere in the corrected geometry. This describes the Kondo model in terms
of a geometric transition. A dual matrix model reflects the basic properties of
the corrected gravity solution in its eigenvalue distribution.Comment: 46 pages, 2 figures. Minor typos correcte
Entanglement entropy of Wilson surfaces from bubbling geometries in M-theory
We consider solutions of eleven-dimensional supergravity constructed in [1,2]
that are half-BPS, locally asymptotic to and are the
holographic dual of heavy Wilson surfaces in the six-dimensional
theory. Using these bubbling solutions we calculate the holographic
entanglement entropy for a spherical entangling surface in the presence of a
planar Wilson surface. In addition, we calculate the holographic stress tensor
and, by evaluating the on-shell supergravity action, the expectation value of
the Wilson surface operator.Comment: 42 pages, 4 figures, v2: minor modification
5-dim Superconformal Index with Enhanced En Global Symmetry
The five-dimensional supersymmetric gauge theory with Sp(N)
gauge group and SO(2N_f) flavor symmetry describes the physics on N D4-branes
with D8-branes on top of a single O8 orientifold plane in Type I' theory.
This theory is known to be superconformal at the strong coupling limit with the
enhanced global symmetry for . In this work we calculate
the superconformal index on for the Sp(1) gauge theory by the
localization method and confirm such enhancement of the global symmetry at the
superconformal limit for to a few leading orders in the chemical
potential. Both perturbative and (anti)instanton contributions are present in
this calculation. For cases some issues related the pole structure of
the instanton calculation could not be resolved and here we could provide only
some suggestive answer for the leading contributions to the index. For the
Sp(N) case, similar issues related to the pole structure appear.Comment: 70 pages, references added, published versio