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Register a new userHolographic Wilson Loops in Symmetric Representations in N = 2* Super-Yang-Mills Theory
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We construct the D3-brane solution in the holographic dual of the N = 2* theory that describes Wilson lines in symmetric representations of the gauge group. The results perfectly agree with the direct field-theory predictions based on localization.
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The N=2* Super-Yang-Mills theory (SYM*) undergoes an infinite sequence of large-N quantum phase transitions. We compute expectation values of Wilson loops in k-symmetric and antisymmetric representations of the SU(N) gauge group in this theory and show that the same phenomenon that causes the phase transitions at finite coupling leads to a non-analytic dependence of Wilson loops on k/N when the coupling is strictly infinite, thus making the higher-representation Wilson loops ideal holographic probes of the non-trivial phase structure of SYM*.
We consider double-winding, triple-winding and multiple-winding Wilson loops in the $SU(N)$ Yang-Mills gauge theory. We examine how the area law falloff of the vacuum expectation value of a multiple-winding Wilson loop depends on the number of color $N$. In sharp contrast to the difference-of-areas law recently found for a double-winding $SU(2)$ Wilson loop average, we show irrespective of the spacetime dimensionality that a double-winding $SU(3)$ Wilson loop follows a novel area law which is neither difference-of-areas nor sum-of-areas law for the area law falloff and that the difference-of-areas law is excluded and the sum-of-areas law is allowed for $SU(N)$ ($N ge 4$), provided that the string tension obeys the Casimir scaling for the higher representations. Moreover, we extend these results to arbitrary multi-winding Wilson loops. Finally, we argue that the area law follows a novel law, which is neither sum-of-areas nor difference-of-areas law when $Nge 3$. In fact, such a behavior is exactly derived in the $SU(N)$ Yang-Mills theory in the two-dimensional spacetime.
We find a formulation of $mathcal{N}=2$ supersymmetric Yang-Mills theory in Projective superspace. In particular we find an expression for the field strength in terms of an unconstrained prepotential which is desirable when quantizing the theory. We use this to write the action in terms of the prepotential and show that it reduces to the known result in the abelian limit.
We study event shapes in N=4 SYM describing the angular distribution of energy and R-charge in the final states created by the simplest half-BPS scalar operator. Applying the approach developed in the companion paper arXiv:1309.0769, we compute these observables using the correlation functions of certain components of the N=4 stress-tensor supermultiplet: the half-BPS operator itself, the R-symmetry current and the stress tensor. We present master formulas for the all-order event shapes as convolutions of the Mellin amplitude defining the correlation function of the half-BPS operators, with a coupling-independent kernel determined by the choice of the observable. We find remarkably simple relations between various event shapes following from N=4 superconformal symmetry. We perform thorough checks at leading order in the weak coupling expansion and show perfect agreement with the conventional calculations based on amplitude techniques. We extend our results to strong coupling using the correlation function of half-BPS operators obtained from the AdS/CFT correspondence.
We study two-point functions of single-trace half-BPS operators in the presence of a supersymmetric Wilson line in $mathcal{N}=4$ SYM. We use inversion formula technology in order to reconstruct the CFT data starting from a single discontinuity of the correlator. In the planar strong coupling limit only a finite number of conformal blocks contributes to the discontinuity, which allows us to obtain elegant closed-form expressions for two-point functions of single-trace operators $mathcal{O}_J$ of weight $J=2,3,4$. Our final result passes a number of non-trivial consistency checks: it has the correct discontinuity, it satisfies the superconformal Ward identities, it has a sensible expansion in both defect and bulk OPEs, and is consistent with available results coming from localization. The method is completely algorithmic and can be implemented to calculate correlators of arbitrary weight.
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