TY - JOUR

T1 - Statistical mechanics of vortices from D-branes and T-duality

AU - Eto, Minoru

AU - Fujimori, Toshiaki

AU - Nitta, Muneto

AU - Ohashi, Keisuke

AU - Ohta, Kazutoshi

AU - Sakai, Norisuke

N1 - Funding Information:
This work is supported in part by Grant-in-Aid for Scientific Research from the Ministry of Education, Culture, Sports, Science and Technology, Japan Nos. 17540237 and 18204024 (NS). K. Ohta is supported in part by the 21st Century COE Program at Tohoku University “Exploring New Science by Bridging Particle-Matter Hierarchy”. The work of K. Ohashi and M.E. is supported by Japan Society for the Promotion of Science under the Post-doctoral Research Program. T.F. gratefully acknowledges support from a 21st Century COE Program at Tokyo Tech “Nanometer-Scale Quantum Physics” by the Ministry of Education, Culture, Sports, Science and Technology, and support from the Iwanami Fujukai Foundation. The authors thank the Yukawa Institute for Theoretical Physics at Kyoto University. Discussions during the YITP workshop YITP-W-06-11 on “String Theory and Quantum Field Theory” were useful to complete this work. K. Ohta would like to thank S. Matsuura for useful discussions and comments.

PY - 2008/1/14

Y1 - 2008/1/14

N2 - We propose a novel and simple method to compute the partition function of statistical mechanics of local and semi-local BPS vortices in the Abelian-Higgs model and its non-Abelian extension on a torus. We use a D-brane realization of the vortices and T-duality relation to domain walls. We use a special limit where domain walls reduce to gas of hard (soft) one-dimensional rods for Abelian (non-Abelian) cases. In the simpler cases of the Abelian-Higgs model on a torus, our results agree with exact results which are geometrically derived by an explicit integration over the moduli space of vortices. The equation of state for U (N) gauge theory deviates from van der Waals one, and the second virial coefficient is proportional to 1 / sqrt(N), implying that non-Abelian vortices are "softer" than Abelian vortices. Vortices on a sphere are also briefly discussed.

AB - We propose a novel and simple method to compute the partition function of statistical mechanics of local and semi-local BPS vortices in the Abelian-Higgs model and its non-Abelian extension on a torus. We use a D-brane realization of the vortices and T-duality relation to domain walls. We use a special limit where domain walls reduce to gas of hard (soft) one-dimensional rods for Abelian (non-Abelian) cases. In the simpler cases of the Abelian-Higgs model on a torus, our results agree with exact results which are geometrically derived by an explicit integration over the moduli space of vortices. The equation of state for U (N) gauge theory deviates from van der Waals one, and the second virial coefficient is proportional to 1 / sqrt(N), implying that non-Abelian vortices are "softer" than Abelian vortices. Vortices on a sphere are also briefly discussed.

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U2 - 10.1016/j.nuclphysb.2007.06.020

DO - 10.1016/j.nuclphysb.2007.06.020

M3 - Article

AN - SCOPUS:35648979116

SN - 0550-3213

VL - 788

SP - 120

EP - 136

JO - Nuclear Physics B

JF - Nuclear Physics B

IS - 3

ER -