Symmetric Wilson Loops Research Articles

Comments on higher rank Wilson loops in mathcal{N} = 2\u2217

For mathcal{N} = 2∗ theory with U(N ) gauge group we evaluate expectation values of Wilson loops in representations described by a rectangular Young tableau with n rows and k columns. The evaluation reduces to a two-matrix model and we explain, using a combination of numerical and analytical techniques, the general properties of the eigen-value distributions in various regimes of parameters (N, λ, n, k) where λ is the ’t Hooft coupling. In the large N limit we present analytic results for the leading and sub-leading contributions. In the particular cases of only one row or one column we reproduce previously known results for the totally symmetry and totally antisymmetric representations. We also extensively discusss the mathcal{N} = 4 limit of the mathcal{N} = 2∗ theory. While establishing these connections we clarify aspects of various orders of limits and how to relax them; we also find it useful to explicitly address details of the genus expansion. As a result, for the totally symmetric Wilson loop we find new contributions that improve the comparison with the dual holographic computation at one loop order in the appropriate regime.

Symmetric Wilson Loops beyond leading order

We study the circular Wilson loop in the symmetric representation of U(N)U(N) in mathcal{N} = 4𝒩=4 super-Yang-Mills (SYM). In the large NN limit, we computed the exponentially-suppressed corrections for strong coupling, which suggests non-perturbative physics in the dual holographic theory. We also computed the next-to-leading order term in 1/N1/N, and the result matches with the exact result from the kk-fundamental representation.

Large rank Wilson loops in $ \mathcal{N} = 2 $ superconformal QCD at strong coupling

We compute the expectation values of circular Wilson loops in large representations at strong coupling, in the large-N limit of the N=2 superconformal theory with SU(N) gauge group and 2N hypermultiplets. Employing Pestun's matrix integral, we focus attention on symmetric and antisymmetric representations with ranks of order N. We find that large rank antisymmetric loops are independent of the coupling at strong 't Hooft coupling while symmetric Wilson loops grow exponentially with it. Symmetric loops display a non-analyticity as a function of the rank, characterized by the splitting of a single matrix model eigenvalue from the continuum, bearing close resemblance to Bose-Einstein condensation in an ideal gas. We discuss implications of these for a putative large-N string dual. The method of calculation we adopt makes explicit the connection to Fermi and Bose gas descriptions and also suggests a tantalizing connection of the above system to a multichannel Kondo model.

HOLOGRAPHY OF ROTATING DUAL GIANT WILSON LOOPS

We briefly review a tunneling picture of rotating D3-brane solutions. By applying the "double Wick rotation" to the Lorentzian solutions, we construct Euclidean solutions. The solutions are composed of dual giant gravitons and spike D3-brane solutions, and their classical actions reproduce expectation values of the k-th symmetric Wilson loops as well as correlation functions of dual giant graviton operators as expected.

A tunneling picture of dual giant Wilson loop

We further discuss a rotating dual giant Wilson loop (D3-brane) solution constructed in Lorentzian AdS by Drukker et al. The solution is shown to be composed of a dual giant Wilson loop and a dual giant graviton by minutely examining its shape. Hence it may be supposed that the dual gauge-theory operator should be a k-th symmetric Wilson loop with insertions of dual giant graviton operators. To give a convincing argument for this observation, the classical action of the solution should be evaluated in Euclidean signature. For this purpose we perform a Wick rotation to the Lorentzian solution by following the tunneling prescription and obtain Euclidean solutions attaching to a circle or a straight line on the AdS boundary. The classical action contains a logarithmic divergence which is proportional to the R-charge. It is consistent with the correlation function of the dual giant graviton operators. Because of ambiguities concerning regularization, finite terms of the action do not lead to conclusive evidence. However we may expect that the ambiguities would cancel by subtracting the action of the D3-brane with a straight-line boundary from that with a circular boundary. It is really shown that the difference is consistent with the expectation value of the k-th symmetric Wilson loop. Although our analysis does not specify the unique dual gauge-theory operator, we discuss possible candidates implied by the D3-brane computation.

Semi-classical open string corrections and symmetric Wilson loops

In the AdS/CFT correspondence, an AdS_2 x S^2 D3-brane with electric flux in AdS_5 x S^5 spacetime corresponds to a circular Wilson loop in the symmetric representation or a multiply wound one in N=4 super Yang-Mills theory. In order to distinguish the symmetric loop and the multiply wound loop, one should see an exponentially small correction in large 't Hooft coupling. We study semi-classically the disk open string attached to the D3-brane. We obtain the exponent of the term and it agrees with the result of the matrix model calculation of the symmetric Wilson loop.

Spacelike Wilson loops at finite temperature

In the high temperature phase of Yang-Mills theories, large spatial Wilson loops show area law behaviour with a string tension that grows with increasing temperature. Within the framework of the commonly used string picture we use a large scale expansion, which allows us to determine the string tension from measurements of intermediate and symmetric Wilson loops.