Phases of thermal 𝒩 = 2 quiver gauge theories

2007/08/31 by Kasper J. Larsen, Niels A. Obers · 7 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Eigenvalues and eigenvectors #Gauge theory #Geometry #Mathematical physics #Mathematics #Order (exchange) #Particle physics theoretical and experimental studies #Phase (matter) #Phase diagram #Phase transition #Physics #Pure mathematics #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #Quiver #Scalar (mathematics) #hep-th

paper · pdf · doi:10.1088/1126-6708/2008/01/057

published in Journal of High Energy Physics 2008(01), 057 (Springer Nature) · 40 pages text + 15 pages appendix, 3 figures, latex; v2: one minor typo corrected and typeset in JHEP format; v3: computation of saddle points in Sec. 4.2 improved, discussion of stability of saddle points added in Sec. 6.2, minor changes, ref. added

openalex publication_date 2008/01/28 · arxiv created 2008/01/30 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We consider large N U(N)^M thermal N=2 quiver gauge theories on S¹ x S³. We obtain a phase diagram of the theory with R-symmetry chemical potentials, separating a low-temperature/high-chemical potential region from a high-temperature/low-chemical potential region. In close analogy with the N=4 SYM case, the free energy is of order O(1) in the low-temperature region and of order O(N² M) in the high-temperature phase. We conclude that the N=2 theory undergoes a first order Hagedorn phase transition at the curve in the phase diagram separating these two regions. We observe that in the region of zero temperature and critical chemical potential the Hilbert space of gauge invariant operators truncates to smaller subsectors. We compute a l-loop effective potential with non-zero VEV's for the scalar fields in a sector where the VEV's are homogeneous and mutually commuting. At low temperatures the eigenvalues of these VEV's are distributed uniformly over an S⁵/Z_M which we interpret as the emergence of the S⁵/Z_M factor of the holographically dual geometry AdS₅ x S⁵/Z_M. Above the Hagedorn transition the eigenvalue distribution of the Polyakov loop opens a gap, resulting in the collapse of the joint eigenvalue distribution from S⁵/Z_M x S¹ into S⁶/Z_M.

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