Branes from light: embeddings and energetics for symmetric k-quarks in N = 4 $$ \mathcal{N}=4 $$ SYM

Abstract

Abstract:We construct the D3-brane dual to a k-quark of N = 4 super-Yang-Mills theory in the totally symmetric representation of SU(N ), undergoing arbitrary motion. Our method of construction generalizes previous work by Mikhailov, and proceeds by shooting light rays inward from the anti-de Sitter boundary, to trace out the brane embedding. We expect this method to have wider relevance, and provide evidence for this by showing that it correctly reproduces the known D5-brane embeddings dual to totally antisymmetric k-quarks. As an application of our solutions, we compute the energy of the D3-brane and extract from it the k-quark's intrinsic energy and rate of radiation. The result matches expectations based on previous calculations, and makes contact with the exact Bremsstrahlung function for the fundamental representation.

Cusp anomalous dimension and rotating open strings in AdS/CFT

“…We have covered the case when the Wilson loop is in the fundamental representation, a "quark" with mass m q . Could be also worth explore the generalisation to the case of D3-branes [20,21] (symmetric representation) and D5-brane (antisymmetric representation). We plan to investigate this issue in a future work.…”

Higher rank Wilson loops in N = 2∗ super-Yang-Mills theory

“…Wilson loops of rank k ∼ N are dual to D-brane configurations carrying the fundamental string charge [18][19][20][21][22][23][24], and have been extensively studied in the N = 4 super-Yang-Mills theory [19,23,[25][26][27][28][29][30], for which the matrix model is just Gaussian [31,32]. As far as N = 2 theories are concerned, higher-rank Wilson loops have been calculated for the N = 2 superconformal QCD [33], whose solution at strong coupling is known [34] but is very different from that of SYM*.…”

On scalar radiation

“…In the introduction we mentioned that holographic computations of radiation do not completely agree with each other. Our work suggests the following scenario: probe string/brane computations [12][13][14] reproduce the results of a 'minimally coupled' version of the dual CFT, where the improvement term in the energy-momentum tensor is 'turned-off', while backreacted supergravity computations 15,16 yield results that fully agree with the field theory ones when the scalars are conformally coupled.…”

“…In particular, for the conformally coupled scalar it follows that B cc = 8 3 h. This ratio is the same as in Maxwell's theory, eq. (14). The work 10 failed to reproduce this ratio for scalars, because it compared B ξ=0 to h ξ=1/6 .…”

“…Intriguingly, these two methods do not fully agree. At the holographic probe level, the computation of 12 , followed by 13,14 indicated that for a 1/2 BPS probe coupled to N = 4 super Yang-Mills, in the large N , large λ limit, the total radiated power is indeed of the form given by (2). The beautiful works 15,16 dealt with the backreacted holographic computations, see also [17][18][19] .…”