Abstract
We apply the matrix model of Kapustin, Willett and Yaakov to compute the free energy of \( \mathcal{N}=3 \) Chern-Simons matter theories with \( {{\widehat{D}}_n} \) quivers in the large N limit. We conjecture a general expression for the free energy that is explicitly invariant under Seiberg duality and show that it can be interpreted as a sum over certain graphs known as signed graphs. Through the AdS/CFT correspondence, this leads to a prediction for the volume of certain tri-Sasaki Einstein manifolds. We also study the unfolding procedure, which relates these \( {{\widehat{D}}_n} \) quivers to \( {{\widehat{A}}_{2n-5 }} \) quivers. Furthermore, we consider the addition of massive fundamental flavor fields, verifying that integrating these out decreases the free energy in accordance with the F-theorem.
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References
E. Witten, Topological Quantum Field Theory, Commun. Math. Phys. 117 (1988) 353 [INSPIRE].
V. Pestun, Localization of gauge theory on a four-sphere and supersymmetric Wilson loops, Commun. Math. Phys. 313 (2012) 71 [arXiv:0712.2824] [INSPIRE].
A. Kapustin, B. Willett and I. Yaakov, Exact Results for Wilson Loops in Superconformal Chern-Simons Theories with Matter, JHEP 03 (2010) 089 [arXiv:0909.4559] [INSPIRE].
D.L. Jafferis, The Exact Superconformal R-Symmetry Extremizes Z, JHEP 05 (2012) 159 [arXiv:1012.3210] [INSPIRE].
N. Hama, K. Hosomichi and S. Lee, Notes on SUSY Gauge Theories on Three-Sphere, JHEP 03 (2011) 127 [arXiv:1012.3512] [INSPIRE].
J. Kallen and M. Zabzine, Twisted supersymmetric 5D Yang-Mills theory and contact geometry, JHEP 05 (2012) 125 [arXiv:1202.1956] [INSPIRE].
D.L. Jafferis and S.S. Pufu, Exact results for five-dimensional superconformal field theories with gravity duals, arXiv:1207.4359 [INSPIRE].
D.L. Jafferis, I.R. Klebanov, S.S. Pufu and B.R. Safdi, Towards the F-Theorem: N = 2 Field Theories on the Three-Sphere, JHEP 06 (2011) 102 [arXiv:1103.1181] [INSPIRE].
J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [Int. J. Theor. Phys. 38 (1999) 1113] [hep-th/9711200] [INSPIRE].
S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [INSPIRE].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].
N. Drukker, M. Mariño and P. Putrov, From weak to strong coupling in ABJM theory, Commun. Math. Phys. 306 (2011) 511 [arXiv:1007.3837] [INSPIRE].
O. Aharony, O. Bergman, D.L. Jafferis and J. Maldacena, N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals, JHEP 10 (2008) 091 [arXiv:0806.1218] [INSPIRE].
I.R. Klebanov and A.A. Tseytlin, Entropy of near extremal black p-branes, Nucl. Phys. B 475 (1996) 164 [hep-th/9604089] [INSPIRE].
C.P. Herzog, I.R. Klebanov, S.S. Pufu and T. Tesileanu, Multi-Matrix Models and Tri-Sasaki Einstein Spaces, Phys. Rev. D 83 (2011) 046001 [arXiv:1011.5487] [INSPIRE].
D. Martelli and J. Sparks, The large-N limit of quiver matrix models and Sasaki-Einstein manifolds, Phys. Rev. D 84 (2011) 046008 [arXiv:1102.5289] [INSPIRE].
S. Cheon, H. Kim and N. Kim, Calculating the partition function of N = 2 Gauge theories on S 3 and AdS/CFT correspondence, JHEP 05 (2011) 134 [arXiv:1102.5565] [INSPIRE].
D.L. Jafferis and A. Tomasiello, A Simple class of N = 3 gauge/gravity duals, JHEP 10 (2008) 101 [arXiv:0808.0864] [INSPIRE].
D.R. Gulotta, C.P. Herzog and S.S. Pufu, From Necklace Quivers to the F-theorem, Operator Counting and T(U(N)), JHEP 12 (2011) 077 [arXiv:1105.2817] [INSPIRE].
H.-U. Yee, AdS/CFT with Tri-Sasakian Manifolds, Nucl. Phys. B 774 (2007) 232 [hep-th/0612002] [INSPIRE].
B. Assel, C. Bachas, J. Estes and J. Gomis, IIB Duals of D = 3 N = 4 Circular Quivers, JHEP 12 (2012) 044 [arXiv:1210.2590] [INSPIRE].
D.R. Gulotta, J. Ang and C.P. Herzog, Matrix Models for Supersymmetric Chern-Simons Theories with an ADE Classification, JHEP 01 (2012) 132 [arXiv:1111.1744] [INSPIRE].
B. Willett and I. Yaakov, N=2 Dualities and Z Extremization in Three Dimensions, arXiv:1104.0487 [INSPIRE].
F. Benini, C. Closset and S. Cremonesi, Comments on 3d Seiberg-like dualities, JHEP 10 (2011) 075 [arXiv:1108.5373] [INSPIRE].
O. Aharony, IR duality in D = 3 N = 2 supersymmetric USp(2N(c)) and U(N(c)) gauge theories, Phys. Lett. B 404 (1997) 71 [hep-th/9703215] [INSPIRE].
A. Giveon and D. Kutasov, Seiberg Duality in Chern-Simons Theory, Nucl. Phys. B 812 (2009) 1 [arXiv:0808.0360] [INSPIRE].
F. Harary, On the Notion of Balance of a Signed Graph, Michigan Math. J. 2 (1953) 143.
T. Zaslavsky, The Geometry of Root Systems and Signed Graphs, Amer. Math. Monthly 88 (1981) 88.
T. Zaslavsky, Signed Graphs, Discrete Appl. Math. 4 (1982) 47.
S. Chaiken, A Combinatorial Proof of the All Minors Matrix Tree Theorem, SIAM J. Algebra. Discr. 3 (1982) 319.
I.R. Klebanov, S.S. Pufu and B.R. Safdi, F-Theorem without Supersymmetry, JHEP 10 (2011) 038 [arXiv:1105.4598] [INSPIRE].
A. Amariti and M. Siani, Z-extremization and F-theorem in Chern-Simons matter theories, JHEP 10 (2011) 016 [arXiv:1105.0933] [INSPIRE].
I.R. Klebanov, S.S. Pufu, S. Sachdev and B.R. Safdi, Entanglement Entropy of 3-D Conformal Gauge Theories with Many Flavors, JHEP 05 (2012) 036 [arXiv:1112.5342] [INSPIRE].
H. Casini, M. Huerta and R.C. Myers, Towards a derivation of holographic entanglement entropy, JHEP 05 (2011) 036 [arXiv:1102.0440] [INSPIRE].
H. Casini and M. Huerta, On the RG running of the entanglement entropy of a circle, Phys. Rev. D 85 (2012) 125016 [arXiv:1202.5650] [INSPIRE].
D.R. Gulotta, C.P. Herzog and T. Nishioka, The ABCDEF’s of Matrix Models for Supersymmetric Chern-Simons Theories, JHEP 04 (2012) 138 [arXiv:1201.6360] [INSPIRE].
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ArXiv ePrint: 1211.1388
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Crichigno, P.M., Herzog, C.P. & Jain, D. Free energy of \( {{\widehat{D}}_n} \) quiver Chern-Simons theories. J. High Energ. Phys. 2013, 39 (2013). https://doi.org/10.1007/JHEP03(2013)039
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DOI: https://doi.org/10.1007/JHEP03(2013)039