Phases of large N vector Chern-Simons theories on S super(2) S super(1)

• Published in: The journal of high energy physics Vol. 2013; no. 9; pp. 1 - 85
• Main Authors: Jain, Sachin, Minwalla, Shiraz, Sharma, Tarun, Takimi, Tomohisa, Wadia, Spenta R, Yokoyama, Shuichi
• Format: Journal Article
• Language: English
• Published: 01.09.2013
• Subjects: Density; Eigenvalues; Integrals; Mathematical analysis; Mathematical models; Partitions; Phases
• ISSN: 1029-8479
• DOI: 10.1007/JHEP09(2013)009

(ProQuest: ... denotes formulae and/or non-USASCII text omitted; see image).We study the thermal partition function of level k U(N) Chern-Simons theories on S super(2) interacting with matter in the fundamental representation. We work in the 't Hooft limit, ..., with ... and ... held fixed where T is the temperature and V sub(2) the volume of the sphere. An effective action proposed in arXiv:1211.4843 relates the partition function to the expectation value of a 'potential' function of the S super(1) holonomy in pure Chern-Simons theory; in several examples we compute the holonomy potential as a function of lambda . We use level-rank duality of pure Chern-Simons theory to demonstrate the equality of thermal partition functions of previously conjectured dual pairs of theories as a function of the temperature. We reduce the partition function to a matrix integral over holonomies. The summation over flux sectors quantizes the eigenvalues of this matrix in units of ... and the eigenvalue density of the holonomy matrix is bounded from above by ... The corresponding matrix integrals generically undergo two phase transitions as a function of temperature. For several Chern-Simons matter theories we are able to exactly solve the relevant matrix models in the low temperature phase, and determine the phase transition temperature as a function of lambda . At low temperatures our partition function smoothly matches onto the N and lambda independent free energy of a gas of non renormalized multi trace operators. We also find an exact solution to a simple toy matrix model; the large N Gross-Witten-Wadia matrix integral subject to an upper bound on eigenvalue density.