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We study the relation between 5D super Yang–Mills theory and the holographic description of 6D (2, 0) superconformal theory. We start by clarifying some issues related to the localization of SYM with matter on S5. We concentrate on the case of a single adjoint hypermultiplet with a mass term and argue that the theory has a symmetry enlargement at mass M = 1/(2r), where r is the S5 radius. However, in order to have a well-defined localization locus it is necessary to rotate M onto the imaginary axis, breaking the enlarged symmetry. Based on our prescription, the imaginary mass values are physical and we show how the localized path integral is consistent with earlier results for 5D SYM in flat space. We then compute the free energy and the expectation value for a circular Wilson loop in the large N limit. The Wilson loop calculation shows a mass dependent constant rescaling between weak and strong coupling. The Wilson loop continued back to to the enlarged symmetry point is consistent with a supergravity computation for an M2 brane using the standard identification of the compactification radius and the 5D coupling. If we continue back to the physical regime and use this value of the mass to determine the compactification radius, then we find agreement between the SYM free energy and the corresponding supergravity calculation. We also verify numerically some of our analytic approximations.

We evaluate the large-N behavior of the superconformal indices of toric quiver gauge theories, and use it to find the entropy functions of the dual electrically charged rotating AdS 5 black holes. To this end, we employ the recently proposed Bethe Ansatz method, and find a certain set of solutions to the Bethe Ansatz Equations of toric theories. This, in turn, allows us to compute the large-N behavior of the index for these theories, including the infinite families Y pq , X pq and L pqr of quiver gauge theories. Our results are in perfect agreement with the predictions made recently using the Cardy-like limit of the superconformal index. We also explore the index structure in the space of chemical potentials and describe the pattern of Stokes lines arising in the conifold theory case.

We compute the QCD phase diagram in the plane of the chiral chemical potential and temperature using the linear sigma model coupled to quarks and to the Polyakov loop. The chiral chemical potential accounts for effects of imbalanced chirality due to QCD sphaleron transitions which may emerge in heavy-ion collisions. We found three effects caused by the chiral chemical potential: the imbalanced chirality (i) tightens the link between deconfinement and chiral phase transitions; (ii) lowers the common critical temperature; (iii) strengthens the order of the phase transition by converting the crossover into the strong first order phase transition passing via the second order end-point. Since the fermionic determinant with the chiral chemical potential has no sign problem, the chirally imbalanced QCD matter can be studied in numerical lattice simulations.Comment: 6 pages, 4 figures, RevTeX 4.