37 research outputs found
WiLE: a Mathematica package for weak coupling expansion of Wilson loops in ABJ(M) theory
We present WiLE, a Mathematica package designed to perform the weak coupling
expansion of any Wilson loop in ABJ(M) theory at arbitrary perturbative order.
For a given set of fields on the loop and internal vertices, the package
displays all the possible Feynman diagrams and their integral representations.
The user can also choose to exclude non planar diagrams, tadpoles and
self-energies. Through the use of interactive input windows, the package should
be easily accessible to users with little or no previous experience. The
package manual provides some pedagogical examples and the computation of all
ladder diagrams at three-loop relevant for the cusp anomalous dimension in
ABJ(M). The latter application gives also support to some recent results
computed in different contexts.Comment: 35 pages, 4 figures and 1 table, comments added. To appear in Comput.
Phys. Commu
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
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
Regge spectroscopy of higher twist states in supersymmetric Yang-Mills theory
We study a family of higher-twist Regge trajectories in
supersymmetric Yang-Mills theory using the Quantum Spectral Curve. We explore
the many-sheeted Riemann surface connecting the different trajectories and show
the interplay between the degenerate non-local operators known as horizontal
trajectories. We resolve their degeneracy analytically by computing the first
non-trivial order of the Regge intercept at weak coupling, which exhibits new
behaviour: it depends linearly on the coupling. This is consistent with our
numerics, which interpolate all the way to strong coupling.Comment: main text: 6 pages, 5 figures; supplemental material: 17 pages, 3
figures, 3 table
Towards the exact Bremsstrahlung function of ABJM theory
We present the three-loop calculation of the Bremsstrahlung function
associated to the 1/2-BPS cusp in ABJM theory, including color subleading
corrections. Using the BPS condition we reduce the computation to that of a
cusp with vanishing angle. We work within the framework of heavy quark
effective theory (HQET) that further simplifies the analytic evaluation of the
relevant cusp anomalous dimension in the near-BPS limit. The result passes
nontrivial tests, such as exponentiation, and is in agreement with the
conjecture made in [1] for the exact expression of the Bremsstrahlung function,
based on the relation with fermionic latitude Wilson loops.Comment: 46 pages, 15 figure