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Register a new userN = 2* Phase Transitions and Holography
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We clarify the relationship between probe analysis of the supergravity dual and the large-N solution of the localization matrix model for the planar N = 2* super-Yang-Mills theory. A formalism inspired by supergravity allows us to systematically solve the matrix model at strong coupling. Quite surprisingly, we find that quantum phase transitions, known to occur in the N = 2* theory, start to be visible at the third order of the strong-coupling expansion and thus constitute a perturbative phenomenon on the string worldsheet.
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We study phase transitions driven by fermionic double-trace deformations in gauge-gravity duality. Both the strength of the double trace deformation and the infrared conformal dimension/self-energy scaling of the quasiparticle can be used to decrease the critical temperature to zero, leading to a line of quantum critical points. The self-energy scaling is controlled indirectly through an applied magnetic field and the quantum phase transition naturally involves the condensation of a fermion bilinear which models the spin density wave in an antiferromagnetic state. The nature of the quantum critical points depends on the parameters and we find either a Berezinskii-Kosterlitz-Thouless-type transition or one of two distinct second order transitions with non-mean field exponents. One of these is an anomalous branch where the order parameter of constituent non-Fermi liquid quasiparticles is enhanced by the magnetic field. Stabilization of ordered non-Fermi liquids by a strong magnetic field is observed in experiments with highly oriented pyrolytic graphite.
We consider $mathcal{N}=2$ superconformal quiver gauge theories in four dimensions and evaluate the chiral/anti-chiral correlators of single-trace operators. We show that it is convenient to form particular twisted and untwisted combinations of these operators suggested by the dual holographic description of the theory. The various twisted sectors are orthogonal and the correlators in each sector have always the same structure, as we show at the lowest orders in perturbation theory with Feynman diagrams. Using localization we then map the computation to a matrix model. In this way we are able to obtain formal expressions for the twisted correlators in the planar limit that are valid for all values of the t Hooft coupling $lambda$, and find that they are proportional to $1/lambda$ at strong coupling. We successfully test the correctness of our extrapolation against a direct numerical evaluation of the matrix model and argue that the $1/lambda$ behavior qualitatively agrees with the holographic description.
The counting of microstates of BPS black-holes on local Calabi-Yau of the form ${mathcal O}(p-2)oplus{mathcal O}(-p) longrightarrow S^2$ is explored by computing the partition function of q-deformed Yang-Mills theory on $S^2$. We obtain, at finite $N$, the instanton expansion of the gauge theory. It can be written exactly as the partition function for U(N) Chern-Simons gauge theory on a Lens space, summed over all non-trivial vacua, plus a tower of non-perturbative instanton contributions. In the large $N$ limit we find a peculiar phase structure in the model. At weak string coupling the theory reduces to the trivial sector and the topological string partition function on the resolved conifold is reproduced in this regime. At a certain critical point, instantons are enhanced and the theory undergoes a phase transition into a strong coupling regime. The transition from the strong coupling phase to the weak coupling phase is of third order.
Utilizing the large N dual description of a metastable system of branes and anti-branes wrapping rigid homologous S^2s in a non-compact Calabi-Yau threefold, we study phase transitions induced by changing the positions of the S^2s. At leading order in 1/N the effective potential for this system is computed by the planar limit of an auxiliary matrix model. Beginning at the two loop correction, the degenerate vacuum energy density of the discrete confining vacua split, and a potential is generated for the axion. Changing the relative positions of the S^2s causes discrete jumps in the energetically preferred confining vacuum and can also obstruct direct brane/anti-brane annihilation processes. The branes must hop to nearby S^2s before annihilating, thus significantly increasing the lifetime of the corresponding non-supersymmetric vacua. We also speculate that misaligned metastable glueball phases may generate a repulsive inter-brane force which stabilizes the radial mode present in compact Calabi-Yau threefolds.
We propose a general formula for the perturbative large N superconformal index of 5d quiver fixed point theories that have an AdS(6)xS(4)/Z(n) supergravity dual. This index is obtained from the parent theory by projecting to orbifold-invariant states and adding the twisted sector contributions. Our result agrees with expectations from the dual supergravity description. We test our formula against the direct computation of the index for Z(2) and Z(3) and find complete agreement.
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