96 research outputs found
Correlators of chiral primaries and 1/8 BPS Wilson loops from perturbation theory
We study at perturbative level the correlation functions of a general class
of 1/8 BPS Wilson loops and chiral primaries in N = 4 Super Yang-Mills theory.
The contours and the location of operator insertions share a sphere S^2
embedded into spacetime and the system preserves at least two supercharges. We
perform explicit two-loop computations, for some particular but still rather
general configuration, that confirm the elegant results expected from
localization procedure. We find notably full consistency with the multi-matrix
model averages, obtained from 2D Yang-Mills theory on the sphere, when
interacting diagrams do not cancel and contribute non-trivially to the final
answer.Comment: 30 pages, 13 figure
Instantons, Fluxons and Open Gauge String Theory
We use the exact instanton expansion to illustrate various string
characteristics of noncommutative gauge theory in two dimensions. We analyse
the spectrum of the model and present some evidence in favour of Hagedorn and
fractal behaviours. The decompactification limit of noncommutative torus
instantons is shown to map in a very precise way, at both the classical and
quantum level, onto fluxon solutions on the noncommutative plane. The
weak-coupling singularities of the usual Gross-Taylor string partition function
for QCD on the torus are studied in the instanton representation and its double
scaling limit, appropriate for the mapping onto noncommutative gauge theory, is
shown to be a generating function for the volumes of the principal moduli
spaces of holomorphic differentials. The noncommutative deformation of this
moduli space geometry is described and appropriate open string interpretations
are proposed in terms of the fluxon expansion.Comment: 70 pages, 6 figure
Surprises from the resummation of ladders in the ABJ(M) cusp anomalous dimension
We study the cusp anomalous dimension in N=6 ABJ(M) theory, identifying a
scaling limit in which the ladder diagrams dominate. The resummation is encoded
into a Bethe-Salpeter equation that is mapped to a Schroedinger problem,
exactly solvable due to the surprising supersymmetry of the effective
Hamiltonian. In the ABJ case the solution implies the diagonalization of the
U(N) and U(M) building blocks, suggesting the existence of two independent cusp
anomalous dimensions and an unexpected exponentiation structure for the related
Wilson loops. While consistent with previous perturbative analysis, the strong
coupling limit of our result does not agree with the string theory computation,
emphasizing a difference with the analogous resummation in the N=4 case.Comment: 26 pages, 4 figures, references added, published versio
Bremsstrahlung function, leading Luscher correction at weak coupling and localization
We discuss the near BPS expansion of the generalized cusp anomalous dimension
with L units of R-charge. Integrability provides an exact solution, obtained by
solving a general TBA equation in the appropriate limit: we propose here an
alternative method based on supersymmetric localization. The basic idea is to
relate the computation to the vacuum expectation value of certain 1/8 BPS
Wilson loops with local operator insertions along the contour. These
observables localize on a two-dimensional gauge theory on S^2, opening the
possibility of exact calculations. As a test of our proposal, we reproduce the
leading Luscher correction at weak coupling to the generalized cusp anomalous
dimension. This result is also checked against a genuine Feynman diagram
approach in N=4 Super Yang-Mills theory.Comment: 25 pages, 6 figures. References added and typos correcte
Perturbative evaluation of circular 1/2 BPS Wilson loops in N = 6 Super Chern-Simons theories
We present a complete two-loop analysis of the quantum expectation value for
circular BPS Wilson loops in ABJ(M) theories. We examine in details the 1/2 BPS
case, that requires non-trivial fermionic couplings with the contour, finding
perfect agreement with the exact matrix model answer at zero framing. The
result is obtained through a careful application of DRED regularization scheme,
combined with a judicious rearrangement of the relevant perturbative
contributions that reduces the computation to simple integrals. We carefully
analyze the contribution of fermions that is crucial for the consistency with
the localization procedure and point out the arising of pivotal evanescent
terms, discussing their meaning in relation to Ward identities.Comment: 32 pages, 5 figures, Referemces adde
Supersymmetric Wilson loops at two loops
We study the quantum properties of certain BPS Wilson loops in
supersymmetric Yang-Mills theory. They belong to a general family, introduced
recently, in which the addition of particular scalar couplings endows generic
loops on with a fraction of supersymmetry. When restricted to ,
their quantum average has been further conjectured to be exactly computed by
the matrix model governing the zero-instanton sector of YM on the sphere.
We perform a complete two-loop analysis on a class of cusped Wilson loops lying
on a two-dimensional sphere, finding perfect agreement with the conjecture. The
perturbative computation reproduces the matrix-model expectation through a
highly non-trivial interplay between ladder diagrams and self-energies/vertex
contributions, suggesting the existence of a localization procedure.Comment: 35 pages, 14 figures, typos corrected, references adde
Probing Wilson loops in Chern-Simons-matter theories at weak coupling
For three-dimensional super Chern-Simons-matter theories
associated to necklace quivers , we study at quantum level the two kinds of 1/2 BPS Wilson loop operators
recently introduced in arXiv:1506.07614. We perform a two-loop evaluation and
find the same result for the two kinds of operators, so moving to higher loops
a possible quantum uplift of the classical degeneracy. We also compute the 1/4
BPS bosonic Wilson loop and discuss the quantum version of the cohomological
equivalence between fermionic and bosonic Wilson loops. We compare the
perturbative result with the Matrix Model prediction and find perfect matching,
after identification and remotion of a suitable framing factor. Finally, we
discuss the potential appearance of three-loop contributions that might break
the classical degeneracy and briefly analyse possible implications on the BPS
nature of these operators.Comment: 7 pages, 2 figure
Correlators of Hopf Wilson loops in the AdS/CFT correspondence
We study at quantum level correlators of supersymmetric Wilson loops with
contours lying on Hopf fibers of . In SYM theory the
strong coupling analysis can be performed using the AdS/CFT correspondence and
a connected classical string surface, linking two different fibers, is
presented. More precisely, the string solution describes oppositely oriented
fibers with the same scalar coupling and depends on an angular parameter,
interpolating between a non-BPS configuration and a BPS one. The system can be
thought as an alternative deformation of the ordinary antiparallel lines giving
the static quark-antiquark potential, that is indeed correctly reproduced, at
weak and strong coupling, as the fibers approach one another.Comment: 38 pages, 5 figure
A matrix model for the latitude Wilson loop in ABJM theory
In ABJ(M) theory, we propose a matrix model for the exact evaluation of BPS
Wilson loops on a latitude circular contour, so providing a new weak-strong
interpolation tool. Intriguingly, the matrix model turns out to be a particular
case of that computing torus knot invariants in Chern-Simons
theory. At weak coupling we check our proposal against a three-loop
computation, performed for generic framing, winding number and representation.
The matrix model is amenable of a Fermi gas formulation, which we use to
systematically compute the strong coupling and genus expansions. For the
fermionic Wilson loop the leading planar behavior agrees with a previous string
theory prediction. For the bosonic operator our result provides a clue for
finding the corresponding string dual configuration. Our matrix model is
consistent with recent proposals for computing Bremsstrahlung functions exactly
in terms of latitude Wilson loops. As a by-product, we extend the conjecture
for the exact Bremsstrahlung function to generic
representations and test it with a four-loop perturbative computation. Finally,
we propose an exact prediction for at unequal gauge group ranks.Comment: 73 pages; v2: several improvements, JHEP published versio
BPS Wilson loops and Bremsstrahlung function in ABJ(M): a two loop analysis
We study a family of circular BPS Wilson loops in N=6 super
Chern-Simons-matter theories, generalizing the usual 1/2-BPS circle. The scalar
and fermionic couplings depend on two deformation parameters and these
operators can be considered as the ABJ(M) counterpart of the DGRT latitudes
defined in N=4 SYM. We perform a complete two-loop analysis of their vacuum
expectation value, discuss the framing dependence and propose a general
relation with cohomologically equivalent bosonic operators. We make an all-loop
proposal for computing the Bremsstrahlung function associated to the 1/2-BPS
cusp in terms of these generalized Wilson loops. When applied to our two-loop
result it reproduces the known expression. Finally, we comment on the
generalization of this proposal to the bosonic 1/6-BPS case.Comment: 46 pages, 6 figures; references adde
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