Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userTowards the exact Bremsstrahlung function of ABJM theory
76
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
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.
rate research
Read More
In this paper we study the Bremsstrahlung functions for the 1/6 BPS and the 1/2 BPS Wilson lines in ABJM theory. First we use a superconformal defect approach to prove a conjectured relation between the Bremsstrahlung functions associated to the geometric ($B^{varphi}_{1/6}$) and R-symmetry ($B^{theta}_{1/6}$) deformations of the 1/6 BPS Wilson line. This result, non-trivially following from a defect supersymmetric Ward identity, provides an exact expression for $B^{theta}_{1/6}$ based on a known result for $B^{varphi}_{1/6}$. Subsequently, we explore the consequences of this relation for the 1/2 BPS Wilson line and, using the localization result for the multiply wound Wilson loop, we provide an exact closed form for the corresponding Bremsstrahlung function. Interestingly, for the comparison with integrability, this expression appears particularly natural in terms of the conjectured interpolating function $h(lambda)$. During the derivation of these results we analyze the protected defect supermultiplets associated to the broken symmetries, including their two- and three-point correlators.
We construct a class of operators, given by Schur polynomials, in ABJM theory. By computing two point functions at finite $N$ we confirm these are diagonal for this class of operators in the free field limit. We also calculate exact three and multi point correlators in the zero coupling limit. Finally, we consider a particular nontrivial background produced by an operator with an $R$-charge of $O(N^2$. We show that the nonplanar corrections (which can no longer be neglected, even at large $N$) can be resummed to give a $1/(N+M)$ expansion for correlators computed in this background.
In ABJ(M) theory a generalized cusp can be constructed out of the 1/6 BPS Wilson line by introducing an angle $varphi$ in the spacial contour and/or an angle $theta$ in the internal R-symmetry space. The small angles limits of its anomalous dimension are controlled by corresponding Bremsstrahlung functions. In this note we compute the internal space $theta$-Bremsstrahlung function to four loops at weak coupling in the planar limit. Based on this result, we propose an all order conjecture for the $theta$-Bremsstrahlung function.
We consider the Bremsstrahlung function associated to a 1/6-BPS Wilson loop in ABJM theory, with a cusp in the couplings to scalar fields. We non-trivially extend its recent four-loop computation at weak coupling to include non-planar corrections. We have recently proposed a conjecture relating this object to supersymmetric circular Wilson loops with multiple windings, which can be computed via localization. We find agreement between this proposal and the perturbative computation of the Bremsstrahlung function, including color sub-leading corrections. This supports the conjecture and hints at its validity beyond the planar approximation.
In this short note we begin the analysis of deformed integrable Chern-Simons theories. We construct the two loop dilatation operator for the scalar sector of the ABJM theory with $k1 eq -k2$ and we compute the anomalous dimension of some operators.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
