Resumen
Being inspired by the connection between 2D Yang-Mills (YM) theory and (1+1)D “vicious walks” (VW), we consider different incarnations of large-N Douglas-Kazakov (DK) phase transition in gauge field theories and stochastic processes focusing at possible physical interpretations. We generalize the connection between YM and VW, study the influence of initial and final distributions of walkers on the DK phase transition, and describe the effect of the θ-term in corresponding stochastic processes. We consider the Jack stochastic process involving Calogero-type interaction between walkers and investigate the dependence of DK transition point on a coupling constant. Relying on the relation between large-N 2D q-YM and extremal black hole (BH) with large-N magnetic charge, we speculate about a physical interpretation of a DK phase transitions in a 4D extremal charged BH.
| Idioma original | English |
|---|---|
| Número de artículo | 114849 |
| Publicación | Nuclear Physics B |
| Volumen | 950 |
| DOI | |
| Estado | Published - ene 2020 |
Nota bibliográfica
Publisher Copyright:© 2019 The Author(s)
Financiación
We are grateful to K. Bulycheva for the collaboration at the early stage of the work. We would like to thank A. Abanov, Victor Dotsenko, D. Kharzeev, N. Nekrasov, G. Oshanin, J. Policastro, N. Prokof'ev, R. Santachiara, G. Schehr, N. Sopenko, P. Wiegmann, and A. Zhitnitsky for the useful discussions and comments. The work of A.G. was supported by Basis Foundation fellowship No. 17-11-122-1 and RFBR grant 19-02-00214 ; A.G. also thanks Kavli Institute for Theoretical Physics, Santa Barbara and Simons Center for Geometry and Physics for support and hospitality. S.N. acknowledges the support of the Basis Foundation fellowship No. 19-1-1-48-1 . Appendix A q -Deformed 2D Yang-Mills on a sphere S 2 Generalization of the 2D Yang-Mills theory onto the 2D q -Yang-Mills involves the additional parameter q = e − g s , where g s is the string coupling constant. The 2D q -YM theory on a sphere can be mapped onto the nondeformed 2D YM on a cylinder with specific boundary holonomies. The partition function of the q -deformed theory can be written as a sum over representations of the gauge group, as in the non-deformed case. The essential difference is that the dimension of the representation should be replaced by the quantum dimension: (A.1) Z ( q ) ( g , g s , A ) = ∑ R ( dim q R ) 2 − 2 g q A g s 2 N C 2 ( R ) e i θ | R | , where the sum runs again over the representations R , C 1 ( R ) and C 2 ( R ) are the first and the second Casimirs of the representation R , θ is its conjugate value of C 1 ( R ) in the grand canonical ensemble, and the quantum dimension is given in terms of the q -numbers (A.2) dim q R = ∏ i > j [ n i − n j + j − i ] q [ j − i ] q = ∏ i > j sinh g s 2 ( n i − n j + j − i ) sinh g s 2 ( j − i ) . The partition function of the q -Yang-Mills theory on the sphere ( g = 0 ) coincides with the partition function of the non-deformed theory on the cylinder. Recall that for the quantum dimension there exists the following expression: (A.3) dim q R = χ R ( q − ρ ) , ρ i = 1 2 − i . Thus, the partition function of q YM (A.1) coincides with the partition function on a cylinder (11) upon the identification [13–15] : (A.4) θ k = i k g s , g s − 1 = g Y M 2 . Besides, we have to set particles equidistantly in the complex plane since the boundary holonomy is q − ρ . The phase transition for the q YM has richer structure compared to non-deformed case.
| Financiadores | Número del financiador |
|---|---|
| Basis Foundation | 17-11-122-1 |
| S.N. | |
| Kavli Institute for Theoretical Physics, University of California, Santa Barbara | 19-1-1-48-1 |
| Russian Foundation for Basic Research | 19-02-00214 |
ASJC Scopus subject areas
- Nuclear and High Energy Physics
Huella
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