Exact results for static and radiative fields of a quark in $ \mathcal{N} = 4 $ super Yang-Mills

Abstract

In this work (which supersedes our previous preprint [1]) we determine the expectation value of the N = 4 SU(N) SYM Lagrangian density operator in the presence of an infinitely heavy static particle in the symmetric representation of SU(N), by means of a D3-brane probe computation. The result that we obtain coincides with two previous computations of different observables, up to kinematical factors. We argue that these agreements go beyond the D-brane probe approximation, which leads us to propose an exact formula for the expectation value of various operators. In particular, we provide an expression for the total energy loss by radiation of a heavy particle in the fundamental representation.

BPS Wilson loops and Bremsstrahlung function in ABJ(M): a two loop analysis

“…• In conformal field theories Wilson loops allow for computing the energy radiated by a moving quark in the low energy limit (Bremsstrahlung function B(λ)) [47,48] and the contribution to the entanglement entropy due to a heavy quark sitting inside a finite region [49]. The Bremsstrahlung function also governs the small angle expansion of the cusp anomalous dimension Γ cusp (ϕ, θ) B(λ)(θ 2 − ϕ 2 ) for a generalized cusp.…”

Algebraic curve for a cusped Wilson line

“…The first result for the Bremsstrahlung function valid for any coupling was obtained in [6] by relating it to the expectation value of a certain Wilson loop. Shortly after, it was reproduced in [7] by considering a correlation function of a Wilson operator and a local operator. This observable was generalized and computed from the integrability approach in planar N = 4 SYM in the near-BPS regime in [8,9] and [10].…”

Holographic flows and thermodynamics of Polyakov loop impurities

“…The details of the analysis proceed similarly to the D5-brane example, with the one key difference that the D3-brane embedding resides entirely in the non-compact AdS 5 directions and is point-like on the internal S 5 . The corresponding calculation for the expanded, conformal D3-brane solution was performed in [22]. With the non-conformal BPS flow solution, we find that the source term for the dilaton provided by the D3-brane evaluates to: The integral cannot be evaluated analytically.…”

“…Retracing the steps outlined in [22], but now applied to BPS flow embedding, we find that the leading term in the expansion of the rescaled dilaton (3.9) near the boundary z → 0 is:…”