19 research outputs found
BPS Wilson Loops on S^2 at Higher Loops
We consider supersymmetric Wilson loops of the variety constructed by
Drukker, Giombi, Ricci, and Trancanelli, whose spatial contours lie on a
two-sphere. Working to second order in the 't Hooft coupling in planar N=4
Supersymmetric Yang-Mills Theory (SYM), we compute the vacuum expectation value
of a wavy-latitude and of a loop composed of two longitudes. We evaluate the
resulting integrals numerically and find that the results are consistent with
the zero-instanton sector calculation of Wilson loops in 2-d Yang-Mills on S^2
performed by Bassetto and Griguolo. We also consider the connected correlator
of two distinct latitudes to third order in the 't Hooft coupling in planar N=4
SYM. We compare the result in the limit where the latitudes become coincident
to a perturbative calculation in 2-d Yang-Mills on S^2 using a light-cone
Wu-Mandelstam-Leibbrandt prescription. We are not able to calculate the SYM
result at the required order in the separation between the latitudes necessary
for a match with 2-d Yang-Mills; the result, however, does not preclude such a
match.Comment: 39 pages, 15 figures. v2 references added, minor cosmetic changes. v3
minor error in eq. (40) corrected. v4 error in coincident limit of correlator
corrected; claims of disagreement with 2-d Yang-Mills retracte
Wilson Loops in Superconformal Chern-Simons Theory and Fundamental Strings in Anti-de Sitter Supergravity Dual
We study Wilson loop operators in three-dimensional, N=6 superconformal
Chern-Simons theory dual to IIA superstring theory on AdS4 x CP3. Novelty of
Wilson loop operators in this theory is that, for a given contour, there are
two linear combinations of Wilson loop transforming oppositely under
time-reversal transformation. We show that one combination is holographically
dual to IIA fundamental string, while orthogonal combination is set to zero. We
gather supporting evidences from detailed comparative study of generalized
time-reversal transformations in both D2-brane worldvolume and ABJM theories.
We then classify supersymmetric Wilson loops and find at most
1/6-supersymmetry. We next study Wilson loop expectation value in planar
perturbation theory. For circular Wilson loop, we find features remarkably
parallel to circular Wilson loop in N=4 super Yang-Mills theory in four
dimensions. First, all odd loop diagrams vanish identically and even loops
contribute nontrivial contributions. Second, quantum corrected gauge and scalar
propagators take the same form as those of N=4 super Yang-Mills theory.
Combining these results, we propose that expectation value of circular Wilson
loop is given by Wilson loop expectation value in pure Chern-Simons theory
times zero-dimensional Gaussian matrix model whose variance is specified by an
interpolating function of `t Hooft coupling. We suggest the function
interpolates smoothly between weak and strong coupling regime, offering new
test ground of the AdS/CFT correspondence.Comment: v1. 34 pages, 11 figures: v2. major revision, all loop proof added 42
pages, 11 figure
Correlators of Wilson loops and local operators from multi-matrix models and strings in AdS
We study correlation functions of Wilson loops and local operators in a
subsector of N=4 SYM which preserves two supercharges. Localization arguments
allow to map the problem to a calculation in bosonic two-dimensional Yang-Mills
theory. In turn, this can be reduced to computing correlators in certain
Gaussian multi-matrix models. We focus on the correlation function of a Wilson
loop and two local operators, and solve the corresponding three-matrix model
exactly in the planar limit. We compare the strong coupling behavior to string
theory in AdS_5xS^5, finding precise agreement. We pay particular attention to
the case in which the local operators have large R-charge J \sim sqrt{lambda}
at strong coupling.Comment: 50 pages, 9 figures. v2: minor changes, references adde
Impure Aspects of Supersymmetric Wilson Loops
We study a general class of supersymmetric Wilson loops operator in N = 4
super Yang-Mills theory, obtained as orbits of conformal transformations. These
loops are the natural generalization of the familiar circular Wilson-Maldacena
operator and their supersymmetric properties are encoded into a Killing spinor
that is not pure. We present a systematic analysis of their scalar couplings
and of the preserved supercharges, modulo the action of the global symmetry
group, both in the compact and in the non-compact case. The quantum behavior of
their expectation value is also addressed, in the simplest case of the
Lissajous contours: explicit computations at weak-coupling, through Feynman
diagrams expansion, and at strong-coupling, by means of AdS/CFT correspondence,
suggest the possibility of an exact evaluation.Comment: 40 pages, 4 figure
Double-helix Wilson loops: case of two angular momenta
Recently, Wilson loops with the shape of a double helix have played an
important role in studying large spin operators in gauge theories. They
correspond to a quark and an anti-quark moving in circles on an S3 (and
therefore each of them describes a helix in RxS3). In this paper we consider
the case where the particles have two angular momenta on the S3. The string
solution corresponding to such Wilson loop can be found using the relation to
the Neumann-Rosochatius system allowing the computation of the energy and
angular momenta of the configuration. The particular case of only one angular
momentum is also considered. It can be thought as an analytic continuation of
the rotating strings which are dual to operators in the SL(2) sector of N=4
SYM.Comment: 30 pages, 2 figures, LaTeX. v2: Small corrections, reference adde
The generalized cusp in ABJ(M) N = 6 Super Chern-Simons theories
We construct a generalized cusped Wilson loop operator in N = 6 super
Chern-Simons-matter theories which is locally invariant under half of the
supercharges. It depends on two parameters and interpolates smoothly between
the 1/2 BPS line or circle and a pair of antiparallel lines, representing a
natural generalization of the quark-antiquark potential in ABJ(M) theories. For
particular choices of the parameters we obtain 1/6 BPS configurations that,
mapped on S^2 by a conformal transformation, realize a three-dimensional
analogue of the wedge DGRT Wilson loop of N = 4. The cusp couples, in addition
to the gauge and scalar fields of the theory, also to the fermions in the
bifundamental representation of the U(N)xU(M) gauge group and its expectation
value is expressed as the holonomy of a suitable superconnection. We discuss
the definition of these observables in terms of traces and the role of the
boundary conditions of fermions along the loop. We perform a complete two-loop
analysis, obtaining an explicit result for the generalized cusp at the second
non-trivial order, from which we read off the interaction potential between
heavy 1/2 BPS particles in the ABJ(M) model. Our results open the possibility
to explore in the three-dimensional case the connection between localization
properties and integrability, recently advocated in D = 4.Comment: 53 pages, 10 figures, added references, this is the version appeared
on JHE
On the property of Cachazo-Intriligator-Vafa prepotential at the extremum of the superpotential
We consider CIV-DV prepotential F for N=1 SU(n) SYM theory at the extremum of
the effective superpotential and prove the relation Comment: LaTeX, 10 pages; v2: some misprints corrected; v3: submitted to
Phys.Rev.
Localization of the four-dimensional N=4 SYM to a two-sphere and 1/8 BPS Wilson loops
We localize the four-dimensional N=4 super Yang-Mills theory on a four-sphere
to the two-dimensional constrained Hitchin/Higgs-Yang-Mills (cHYM) theory on a
two-sphere S^2. We show that expectation values of certain 1/8 BPS
supersymmetric Wilson loops on S^2 in the 4d N=4 SYM is captured by the 2d cHYM
theory. We further argue that expectation values of Wilson loops in the cHYM
theory agree with the prescription "two-dimensional bosonic Yang-Mills
excluding instanton contributions". Hence, we support the recent conjecture by
Drukker, Giombi, Ricci and Trancanelli on the 1/8 BPS Wilson loops on S^2 in
the 4d N=4 SYM.Comment: 49 pages; v3: typos correcte
Conifolds and Geometric Transitions
Conifold geometries have recieved a lot of attention in string theory and
string-inspired cosmology recently, in particular the Klebanov-Strassler
background that is known as the "warped throat". It is our intention in this
article to give a pedagogical explanation for the singularity resolution in
this geometry and emphasise its connection to geometric transitions. The first
part focuses on the gauge theory dual to the Klebanov-Strassler background,
which we also explain from a T-dual intersecting branes scenario. We then make
the connection to the Gopakumar-Vafa conjecture for open/closed string duality
and summarise a series of papers verifying this model on the supergravity
level.
An appendix provides extensive background material about conifold geometries.
We pay special attention to their complex structures and re-evaluate the
supersymmetry conditions on the background flux in constructions with
fractional D3-branes on the singular (Klebanov-Tseytlin) and resolved (Pando
Zayas-Tseytlin) conifolds. We agree with earlier results that only the singular
solution allows a supersymmetric flux, but point out the importance of using
the correct complex structure to reach this conclusion.Comment: 37 pages, v3: accepted for publication in Reviews of Modern Physic
Flux and Instanton Effects in Local F-theory Models and Hierarchical Fermion Masses
We study the deformation induced by fluxes and instanton effects on Yukawa
couplings involving 7-brane intersections in local F-theory constructions. In
the absence of non-perturbative effects, holomorphic Yukawa couplings do not
depend on open string fluxes. On the other hand instanton effects (or gaugino
condensation on distant 7-branes) do induce corrections to the Yukawas. The
leading order effect may also be captured by the presence of closed string
(1,2) IASD fluxes, which give rise to a non-commutative structure. We check
that even in the presence of these non-perturbative effects the holomorphic
Yukawas remain independent of magnetic fluxes. Although fermion mass
hierarchies may be obtained from these non-perturbative effects, they would
give identical Yukawa couplings for D-quark and Lepton masses in SU(5) F-theory
GUT's, in contradiction with experiment. We point out that this problem may be
solved by appropriately normalizing the wavefunctions. We show in a simple toy
model how the presence of hypercharge flux may then be responsible for the
difference between D-quarks and Lepton masses in local SU(5) GUT's.Comment: 84 pages, 1 figure. v2: minor corrections and references adde