The spectrum of excitations of holographic Wilson loops

Abstract

In the holographic framework, a half BPS Wilson loop in N = 4 supersymmetric Yang-Mills in the fundamental, symmetric or antisymmetric representation of SU (N ), is best described by a fundamental string, a D3 brane or a D5 brane with fluxes in their worldvolumes, respectively. We derive the spectrum of excitations of such D3 brane in AdS 5 × S 5 explicitly, considering its action in both the bosonic and the fermionic sectors, and demonstrate that it is organized according to short multiplets of the supergroup OSp(4 * |4). We also show that the modes of the fundamental string form an ultra-short multiplet of this supergroup. In the case of the D5 brane the bosonic spectrum is only partially known but we argue that it also fills representations of OSp(4 * |4). This way we provide a step towards a unifying picture for the description of holographic excitations of the circular and straight supersymmetric Wilson loops in arbitrary representations. arXiv:1101.5145v3 [hep-th]

Wilson loops and minimal area surfaces in hyperbolic space

“…The quasi-momentum p(λ) is defined from the trace of the monodromy matrix as 12) and determines a set of conserved quantities. However, the monodromy matrix should be trivial.…”

“…Therefore, the condition q n = 0, ∀n ≥ 0 is equivalent to the statement that x i (θ) and ξ i (θ) are the real and imaginary part of the boundary value of the holomorphic function 12) or equivalently to the dispersion relation (A.5). After this brief detour, let us go back to the main problem.…”

“…Much work has been devoted to the computation of explicit examples of Wilson loops. For Euclidean curves, the most studied case is the circular Wilson loop [6][7][8][9][10][11][12][13] although another cases have been considered [14][15][16][17][18]. In the case of Minkowski signature the lightlike cusp [19] turns out to be particularly interesting because of its relation to scattering…”

Line Operator Index on S 1 × S 3

“…Spectrum of fluctuations around the brane is analyzed in [42]. However, in this case, the large N calculation of the field theory index seems difficult since rewriting the character in terms of the Fourier coefficients, ρ n , becomes quickly messy as k increses.…”

Minimal area surfaces in AdSn+1 and Wilson loops

“…There is a large amount of work on the subject, see for example [6][7][8][9][10] and, in particular [11][12][13][14][15][16][17][18][19][20] for the circular Wilson loop, the most studied case. The main interest of this problem is its integrability properties [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36].…”