Wall-crossing, Hitchin systems, and the WKB approximation

被引:244
作者
Gaiotto, Davide [1 ]
Moore, Gregory W. [2 ,3 ]
Neitzke, Andrew [4 ]
机构
[1] Inst Adv Study, Sch Nat Sci, Princeton, NJ 08540 USA
[2] Rutgers State Univ, NHETC, Piscataway, NJ 08855 USA
[3] Rutgers State Univ, Dept Phys & Astron, Piscataway, NJ 08855 USA
[4] Harvard Univ, Dept Phys, Cambridge, MA 02138 USA
基金
美国国家科学基金会;
关键词
Wall-crossing; Donaldson-Thomas invariants; Hitchin systems; Fock-Goncharov coordinates; Hyperkahler geometry; Supersymmetric gauge theory; SUPERCONFORMAL FIELD-THEORIES; SELF-DUAL STRINGS; PROBING F-THEORY; BPS STATES; GAUGE-THEORIES; MODULI SPACE; N=2; MONOPOLES; SPECTRA; COMPACTIFICATION;
D O I
10.1016/j.aim.2012.09.027
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We consider BPS states in a large class of d = 4, N = 2 field theories, obtained by reducing six-dimensional (2, 0) superconformal field theories on Riemann surfaces, with defect operators inserted at points of the Riemann surface. Further dimensional reduction on S-1 yields sigma models, whose target spaces are moduli spaces of Higgs bundles on Riemann surfaces with ramification. In the case where the Higgs bundles have rank 2, we construct canonical Darboux coordinate systems on their moduli spaces. These coordinate systems are related to one another by Poisson transformations associated to BPS states, and have well-controlled asymptotic behavior, obtained from the WKB approximation. The existence of these coordinates implies the Kontsevich-Soibelman wall-crossing formula for the BPS spectrum. This construction provides a concrete realization of a general physical explanation of the wall-crossing formula which was proposed in Gaiotto et al. [40]. It also yields a new method for computing the spectrum using the combinatorics of triangulations of the Riemann surface. (C) 2012 Elsevier Inc. All rights reserved.
引用
收藏
页码:239 / 403
页数:165
相关论文
共 91 条
  • [21] Nahm transform for periodic monopoles and N=2 super Yang-Mills theory
    Cherkis, S
    Kapustin, A
    [J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2001, 218 (02) : 333 - 371
  • [22] Singular monopoles and supersymmetric gauge theories in three dimensions
    Cherkis, SA
    Kapustin, A
    [J]. NUCLEAR PHYSICS B, 1998, 525 (1-2) : 215 - 234
  • [23] CORLETTE K, 1988, J DIFFER GEOM, V28, P361
  • [24] BPS nature of 3-string junctions
    Dasgupta, K
    Mukhi, S
    [J]. PHYSICS LETTERS B, 1998, 423 (3-4) : 261 - 264
  • [25] Denef F, 2000, J HIGH ENERGY PHYS
  • [26] DENEF F, HEPTH0702146
  • [27] Devadoss SatyanL., 2001, Ann. Comb, V5, P71, DOI DOI 10.1007/PL00001293
  • [28] Constraints on the BPS spectrum of Ν=2, D=4 theories with ADE flavor symmetry
    DeWolfe, O
    Hauer, T
    Iqbal, A
    Zwiebach, B
    [J]. NUCLEAR PHYSICS B, 1998, 534 (1-2) : 261 - 274
  • [29] Supersymmetric Yang-Mills theory and integrable systems
    Donagi, R
    Witten, E
    [J]. NUCLEAR PHYSICS B, 1996, 460 (02) : 299 - 334
  • [30] On the relation between Stokes multipliers and the T-Q systems of conformal field theory
    Dorey, P
    Tateo, R
    [J]. NUCLEAR PHYSICS B, 1999, 563 (03) : 573 - 602