Abstract
We propose a new and simple method of estimating the radiation due to an accelerated quark in a strongly coupled medium, within the framework of the anti-de Sitter (AdS)/conformal field theory (CFT) correspondence. In particular, we offer a heuristic explanation of the collimated nature of synchrotron radiation produced by a circling quark, which was recently studied by Athanasiou et al (2010 Phys. Rev. D 81 26001). The gravitational dual of such a quark is a coiling string in AdS, whose backreaction on the spacetime geometry remains tightly confined, as if ‘beamed’ towards the boundary. While this appears to contradict conventional expectations from the scale/radius duality, we resolve the issue by observing that the backreaction of a relativistic string is reproduced by a superposition of gravitational shock waves. We further demonstrate that this proposal allows us to reduce the problem of computing the boundary stress tensor to merely calculating geodesics in AdS, as opposed to solving linearized Einstein's equations.
Highlights
Since its inception 13 years ago, the gauge/gravity duality [1, 2, 3] has engendered vigorous exploration of properties of non-abelian gauge theories by studying their gravitational dual
Let us start by reviewing the essential ingredients of the work of [4], which uses the Anti de Sitter (AdS)/CFT correspondence to study the radiation from a quark in uniform circular motion in a strongly coupled field theory at zero temperature
As we show explicitly in Appendix A, such geodesics form a ‘hemisphere’ in the (x, y, z, u) space, whose equator lies on the boundary u = 0 and whose radius and position is determined by the geometry of the string
Summary
Since its inception 13 years ago, the gauge/gravity duality [1, 2, 3] has engendered vigorous exploration of properties of non-abelian gauge theories by studying their gravitational dual. The radiation pulse does not broaden as it propagates outward, despite the field theory being strongly coupled.3 This result is just as remarkable from the gravitational dual standpoint, since it implies that the backreaction effects from string bits deep in the bulk are somehow ‘beamed’ towards the boundary, contradicting naive expectations from the scale/radius (or UV/IR) duality [7], according to which an excitation deeper in the bulk should be represented by a more dispersed signal in the boundary field theory. We propose a much easier method to obtain the boundary stress tensor, in a straightforward and computationally non-intensive manner which essentially reduces to finding geodesics in AdS This simplification applies to the regime where the string is sufficiently relativistic, which, as we discuss below, includes the present case of interest, and occurs quite generically for bulk dual describing radiation from an accelerating quark.
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