A mathematical formalism for the Kondo effect in Wess-Zumino-Witten branes. (English) Zbl 1144.81357
Summary: In the paper, we adapt our previous formalism for a mathematical treatment of branes to include processes, specifically the Kondo flow for Wess-Zumino-Witten (WZW) branes. In this framework, we give the precise mathematical definitions and formulate a mathematical conjecture relating WZW branes to nonequivariant twisted K-theory in the case of the group \(\mathrm{SU}(n)\). We also discuss regularization of the Kondo flow, thereby giving a first step toward proving our conjecture.
MSC:
| 81T30 | String and superstring theories; other extended objects (e.g., branes) in quantum field theory |
| 19L99 | Topological \(K\)-theory |
References:
| [1] | DOI: 10.1103/PhysRevLett.67.161 · Zbl 0990.81566 · doi:10.1103/PhysRevLett.67.161 |
| [2] | DOI: 10.1103/PhysRevB.48.7297 · doi:10.1103/PhysRevB.48.7297 |
| [3] | Baas N. A., London Mathematical Society Lecture Note Series 308, in: Topology, Geometry and Quantum Field Theory pp 18– |
| [4] | Bakalov B., University Lecture Series 21, in: Lectures on Tensor Categories and Modular Functors (2001) · Zbl 0965.18002 |
| [5] | Ben-Zvi D., Mathematical Surveys and Monographs 88, in: Vertex Algebras and Algebraic Curves, 2. ed. (2004) |
| [6] | DOI: 10.1016/0550-3213(88)90346-X · doi:10.1016/0550-3213(88)90346-X |
| [7] | DOI: 10.1007/BF01232032 · Zbl 0799.17014 · doi:10.1007/BF01232032 |
| [8] | DOI: 10.1016/0550-3213(89)90521-X · doi:10.1016/0550-3213(89)90521-X |
| [9] | DOI: 10.1023/A:1014903315415 · Zbl 1002.81045 · doi:10.1023/A:1014903315415 |
| [10] | DOI: 10.1007/BF01228414 · Zbl 0642.22005 · doi:10.1007/BF01228414 |
| [11] | DOI: 10.1016/j.jpaa.2006.07.006 · Zbl 1119.81384 · doi:10.1016/j.jpaa.2006.07.006 |
| [12] | Frenkel I., Pure and Applied Mathematics 134, in: Vertex operator algebras and the Monster (1988) · Zbl 0674.17001 · doi:10.1016/S0079-8169(08)62324-7 |
| [13] | DOI: 10.1215/S0012-7094-92-06604-X · Zbl 0848.17032 · doi:10.1215/S0012-7094-92-06604-X |
| [14] | DOI: 10.1007/s002200050031 · Zbl 0976.81091 · doi:10.1007/s002200050031 |
| [15] | DOI: 10.1142/S0217751X9000115X · doi:10.1142/S0217751X9000115X |
| [16] | DOI: 10.1007/s00220-004-1202-8 · Zbl 1091.81073 · doi:10.1007/s00220-004-1202-8 |
| [17] | DOI: 10.1016/j.aim.2003.11.012 · Zbl 1071.55004 · doi:10.1016/j.aim.2003.11.012 |
| [18] | DOI: 10.1007/s00220-007-0224-4 · Zbl 1153.17012 · doi:10.1007/s00220-007-0224-4 |
| [19] | DOI: 10.1007/s00220-004-1059-x · Zbl 1083.17010 · doi:10.1007/s00220-004-1059-x |
| [20] | DOI: 10.1142/S0129055X04002163 · Zbl 1078.81052 · doi:10.1142/S0129055X04002163 |
| [21] | DOI: 10.1017/CBO9780511526398.011 · doi:10.1017/CBO9780511526398.011 |
| [22] | DOI: 10.1016/0370-2693(88)91796-0 · doi:10.1016/0370-2693(88)91796-0 |
| [23] | Pressley A., Oxford Mathematical Monographs, in: Loop groups (1986) |
| [24] | DOI: 10.1088/0264-9381/19/22/305 · Zbl 1039.81046 · doi:10.1088/0264-9381/19/22/305 |
| [25] | Segal, G.Topology, Geometry and Quantum Field Theory, London Mathematical Society Lecture Note Series 308 (Cambridge University Press, Cambridge, 2004), pp. 421–577. |
| [26] | DOI: 10.1016/S0550-3213(98)00646-4 · Zbl 0948.81644 · doi:10.1016/S0550-3213(98)00646-4 |
| [27] | Tsuchiya A., Advanced Studies in Pure Mathematics 19 pp 459– (1989) |
| [28] | Turaev V. G., de Gruyter Studies in Mathematics 18, in: Quantum invariants of knots and 3-manifolds (1994) |
| [29] | DOI: 10.1016/0550-3213(88)90603-7 · Zbl 1180.81120 · doi:10.1016/0550-3213(88)90603-7 |
| [30] | DOI: 10.1007/BF01215276 · Zbl 0536.58012 · doi:10.1007/BF01215276 |
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