The Thermal Free Energy in Large N Chern-Simons-Matter Theories
TL;DR: In this paper, the thermal free energy in large N U(N) Chern-Simons-matter theories with matter fields (scalars and/or fermions) in the fundamental representation, in the large temperature limit, was computed.
Abstract: We compute the thermal free energy in large N U(N) Chern-Simons-matter theories with matter fields (scalars and/or fermions) in the fundamental representation, in the large temperature limit. We note that in these theories the eigenvalue distribution of the holonomy of the gauge field along the thermal circle does not localize even at very high temperatures, and this affects the computation significantly. We verify that our results are consistent with the conjectured dualities between Chern-Simons-matter theories with scalar fields and with fermion fields, as well as with the strong-weak coupling duality of the $\mathcal{N}=2$
supersymmetric Chern-Simons-matter theory.
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Technische Universität München1, Novosibirsk State University2, GSI Helmholtz Centre for Heavy Ion Research3, University of Kentucky4, Fermilab5, Washington University in St. Louis6, University of Graz7, University of Vienna8, University of Maryland, College Park9, Max Planck Society10, Vienna University of Technology11, Thomas Jefferson National Accelerator Facility12, Hampton University13, University of Bonn14, University of Washington15, Complutense University of Madrid16, University of Mainz17, Moscow Institute of Physics and Technology18, University of Groningen19, University of Paris-Sud20, Indiana University21, University of California, Davis22, Lawrence Livermore National Laboratory23, University of Helsinki24, University of Virginia25, Istituto Nazionale di Fisica Nucleare26, Forschungszentrum Jülich27, University of Bern28, Warsaw University of Technology29, CERN30, Kent State University31, Utrecht University32, National Research Nuclear University MEPhI33, Lawrence Berkeley National Laboratory34, University of Valencia35, University of Granada36, Brookhaven National Laboratory37, Stony Brook University38, University of Naples Federico II39, University of Santiago de Compostela40, Ruhr University Bochum41, Far Eastern Federal University42
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References
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TL;DR: In this paper, it was shown that 2+1 dimensional quantum Yang-Mills theory with an action consisting purely of the Chern-Simons term is exactly soluble and gave a natural framework for understanding the Jones polynomial of knot theory in three dimensional terms.
Abstract: It is shown that 2+1 dimensional quantum Yang-Mills theory, with an action consisting purely of the Chern-Simons term, is exactly soluble and gives a natural framework for understanding the Jones polynomial of knot theory in three dimensional terms. In this version, the Jones polynomial can be generalized fromS
3 to arbitrary three manifolds, giving invariants of three manifolds that are computable from a surgery presentation. These results shed a surprising new light on conformal field theory in 1+1 dimensions.
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TL;DR: In this paper, the authors constructed three dimensional Chern-Simons-matter theories with gauge groups U(N) × U(n) and SU(N), SU(2) × SU (2) which have explicit = 6 superconformal symmetry.
Abstract: We construct three dimensional Chern-Simons-matter theories with gauge groups U(N) × U(N) and SU(N) × SU(N) which have explicit = 6 superconformal symmetry. Using brane constructions we argue that the U(N) × U(N) theory at level k describes the low energy limit of N M2-branes probing a C4/Zk singularity. At large N the theory is then dual to M-theory on AdS4 × S7/Zk. The theory also has a 't Hooft limit (of large N with a fixed ratio N/k) which is dual to type IIA string theory on AdS4 × CP3. For k = 1 the theory is conjectured to describe N M2-branes in flat space, although our construction realizes explicitly only six of the eight supersymmetries. We give some evidence for this conjecture, which is similar to the evidence for mirror symmetry in d = 3 gauge theories. When the gauge group is SU(2) × SU(2) our theory has extra symmetries and becomes identical to the Bagger-Lambert theory.
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1,260 citations
TL;DR: In this paper, the authors discuss the canonical quantization of the Chern-Simons-Witten theory on several interesting surfaces and the connection to the related two-dimensional theory is illustrated from different points of view.
918 citations
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Abstract: We demonstrate that weakly coupled, large $N, d$-dimensional $SU(N)$ gauge theories on a class of compact spatial manifolds (including $S^{d-1}\times {\rm time}$) undergo deconfinement phase transitions at temperatures proportional to the inverse length scale of the manifold in question The low temperature phase has a free energy of order one, and is characterized by a stringy (Hagedorn) growth in its density of states The high temperature phase has a free energy of order $N^2$ These phases are separated either by a single first order transition that generically occurs below the Hagedorn temperature or by two continuous phase transitions, the first of which occurs at the Hagedorn temperature These phase transitions could perhaps be continuously connected to the usual flat space deconfinement transition in the case of confining gauge theories, and to the Hawking-Page nucleation of $AdS_5$ black holes in the case of the $\mathcal{N}=4$ supersymmetric Yang-Mills theory We suggest that deconfinement transitions may generally be interpreted in terms of black hole formation in a dual string theory Our analysis proceeds by first reducing the Yang-Mills partition function to a $(0+0)$-dimensional integral over a unitary matrix $U$, which is the holonomy (Wilson loop) of the gauge field around the thermal time circle in Euclidean space; deconfinement transitions are large $N$ transitions in this matrix integral
772 citations