The quantum UV-IR map for line defects in \(\mathfrak{gl}(3)\)-type class \(S\) theories. (English) Zbl 1531.81233
Summary: We consider the quantum UV-IR map for line defects in class \(S\) theories of \(\mathfrak{gl}(3)\)-type. This map computes the protected spin character which counts framed BPS states with spin for the bulk-defect system. We give a geometric method of computing this map motivated by the physics of five-dimensional \(\mathcal{N} = 2\) supersymmetric Yang-Mills theory, and compute it explicitly in various examples. As a spin-off we propose a new way of computing a certain specialization of the HOMFLY polynomial for links in \(\mathbb{R}^3\), as a sum over BPS webs attached to the link.
MSC:
| 81T60 | Supersymmetric field theories in quantum mechanics |
| 81T13 | Yang-Mills and other gauge theories in quantum field theory |
| 81T30 | String and superstring theories; other extended objects (e.g., branes) in quantum field theory |
| 81T40 | Two-dimensional field theories, conformal field theories, etc. in quantum mechanics |
| 81Q60 | Supersymmetry and quantum mechanics |
Keywords:
Chern-Simons theories; quantum groups; supersymmetric gauge theory; Wilson loop; ’t Hooft and Polyakov loopsReferences:
| [1] | Neitzke, A.; Yan, F., q-nonabelianization for line defects, JHEP, 09, 153 (2020) · Zbl 1454.81232 · doi:10.1007/JHEP09(2020)153 |
| [2] | Gaiotto, D.; Moore, GW; Neitzke, A., Spectral networks, Annales Henri Poincaré, 14, 1643 (2013) · Zbl 1288.81132 · doi:10.1007/s00023-013-0239-7 |
| [3] | Gaiotto, D.; Witten, E., Knot invariants from four-dimensional gauge theory, Adv. Theor. Math. Phys., 16, 935 (2012) · Zbl 1271.81108 · doi:10.4310/ATMP.2012.v16.n3.a5 |
| [4] | Galakhov, D.; Longhi, P.; Moore, GW, Spectral networks with spin, Commun. Math. Phys., 340, 171 (2015) · Zbl 1344.81141 · doi:10.1007/s00220-015-2455-0 |
| [5] | Gabella, M., Quantum holonomies from spectral networks and framed BPS states, Commun. Math. Phys., 351, 563 (2017) · Zbl 1369.81085 · doi:10.1007/s00220-016-2729-1 |
| [6] | V. Fock and A. Goncharov, Moduli spaces of local systems and higher Teichmüller theory, Publ. Math. Inst. Hautes Études Sci.103 (2006) 1 [math.AG/0311149]. · Zbl 1099.14025 |
| [7] | A. Goncharov and L. Shen, Quantum geometry of moduli spaces of local systems and representation theory, arXiv:1904.10491 [INSPIRE]. |
| [8] | F. Bonahon and H. Wong, Quantum traces for representations of surface groups in SL_2(ℂ), Geom. Topol.15 (2011) 1569 [arXiv:1003.5250]. · Zbl 1227.57003 |
| [9] | D.C. Douglas, Quantum traces for SL_n(ℂ): the case n = 3, arXiv:2101.06817. |
| [10] | K.G. Wilson, Confinement of quarks, Phys. Rev. D10 (1974) 2445 [INSPIRE]. |
| [11] | G. ’t Hooft, On the phase transition towards permanent quark confinement, Nucl. Phys. B138 (1978) 1 [INSPIRE]. |
| [12] | A. Kapustin, Wilson-’t Hooft operators in four-dimensional gauge theories and S-duality, Phys. Rev. D74 (2006) 025005 [hep-th/0501015] [INSPIRE]. |
| [13] | Gomis, J.; Passerini, F., Holographic Wilson loops, JHEP, 08, 074 (2006) · doi:10.1088/1126-6708/2006/08/074 |
| [14] | Pestun, V., Localization of gauge theory on a four-sphere and supersymmetric Wilson loops, Commun. Math. Phys., 313, 71 (2012) · Zbl 1257.81056 · doi:10.1007/s00220-012-1485-0 |
| [15] | D’Hoker, E.; Estes, J.; Gutperle, M., Gravity duals of half-BPS Wilson loops, JHEP, 06, 063 (2007) · doi:10.1088/1126-6708/2007/06/063 |
| [16] | Drukker, N.; Gomis, J.; Okuda, T.; Teschner, J., Gauge theory loop operators and Liouville theory, JHEP, 02, 057 (2010) · Zbl 1270.81134 · doi:10.1007/JHEP02(2010)057 |
| [17] | Drukker, N.; Morrison, DR; Okuda, T., Loop operators and S-duality from curves on Riemann surfaces, JHEP, 09, 031 (2009) · doi:10.1088/1126-6708/2009/09/031 |
| [18] | Gaiotto, D.; Moore, GW; Neitzke, A., Framed BPS states, Adv. Theor. Math. Phys., 17, 241 (2013) · Zbl 1290.81146 · doi:10.4310/ATMP.2013.v17.n2.a1 |
| [19] | Drukker, N.; Gaiotto, D.; Gomis, J., The virtue of defects in 4D gauge theories and 2D CFTs, JHEP, 06, 025 (2011) · Zbl 1298.81170 · doi:10.1007/JHEP06(2011)025 |
| [20] | Y. Ito, T. Okuda and M. Taki, Line operators on S^1 × ℝ^3and quantization of the Hitchin moduli space, JHEP04 (2012) 010 [Erratum ibid.03 (2016) 085] [arXiv:1111.4221] [INSPIRE]. · Zbl 1348.81418 |
| [21] | Aharony, O.; Seiberg, N.; Tachikawa, Y., Reading between the lines of four-dimensional gauge theories, JHEP, 08, 115 (2013) · Zbl 1342.81248 · doi:10.1007/JHEP08(2013)115 |
| [22] | Córdova, C.; Neitzke, A., Line defects, tropicalization, and multi-centered quiver quantum mechanics, JHEP, 09, 099 (2014) · Zbl 1333.81166 · doi:10.1007/JHEP09(2014)099 |
| [23] | Lewkowycz, A.; Maldacena, J., Exact results for the entanglement entropy and the energy radiated by a quark, JHEP, 05, 025 (2014) · Zbl 1390.81606 · doi:10.1007/JHEP05(2014)025 |
| [24] | Gaiotto, D.; Kapustin, A.; Seiberg, N.; Willett, B., Generalized global symmetries, JHEP, 02, 172 (2015) · Zbl 1388.83656 · doi:10.1007/JHEP02(2015)172 |
| [25] | B. Fiol, E. Gerchkovitz and Z. Komargodski, Exact bremsstrahlung function in N = 2 superconformal field theories, Phys. Rev. Lett.116 (2016) 081601 [arXiv:1510.01332] [INSPIRE]. |
| [26] | Moore, GW; Royston, AB; Van den Bleeken, D., Semiclassical framed BPS states, JHEP, 07, 071 (2016) · Zbl 1390.81170 · doi:10.1007/JHEP07(2016)071 |
| [27] | Córdova, C.; Gaiotto, D.; Shao, S-H, Infrared computations of defect Schur indices, JHEP, 11, 106 (2016) · Zbl 1390.81583 · doi:10.1007/JHEP11(2016)106 |
| [28] | L. Bianchi, M. Lemos and M. Meineri, Line defects and radiation in N = 2 conformal theories, Phys. Rev. Lett.121 (2018) 141601 [arXiv:1805.04111] [INSPIRE]. |
| [29] | S. Giombi and S. Komatsu, More exact results in the Wilson loop defect CFT: bulk-defect OPE, nonplanar corrections and quantum spectral curve, J. Phys. A52 (2019) 125401 [arXiv:1811.02369] [INSPIRE]. · Zbl 1507.81172 |
| [30] | Brennan, TD; Dey, A.; Moore, GW, ’t Hooft defects and wall crossing in SQM, JHEP, 10, 173 (2019) · Zbl 1427.81162 · doi:10.1007/JHEP10(2019)173 |
| [31] | Brennan, TD; Dey, A.; Moore, GW, On ’t Hooft defects, monopole bubbling and supersymmetric quantum mechanics, JHEP, 09, 014 (2018) · Zbl 1400.81160 · doi:10.1007/JHEP09(2018)014 |
| [32] | Cirafici, M., Quantum line defects and refined BPS spectra, Lett. Math. Phys., 110, 501 (2019) · Zbl 1453.14132 · doi:10.1007/s11005-019-01226-3 |
| [33] | Ang, JP; Roumpedakis, K.; Seifnashri, S., Line operators of gauge theories on non-spin manifolds, JHEP, 04, 087 (2020) · Zbl 1436.81123 · doi:10.1007/JHEP04(2020)087 |
| [34] | N.B. Agmon and Y. Wang, Classifying superconformal defects in diverse dimensions. Part I. Superconformal lines, arXiv:2009.06650 [INSPIRE]. |
| [35] | Rudelius, T.; Shao, S-H, Topological operators and completeness of spectrum in discrete gauge theories, JHEP, 12, 172 (2020) · Zbl 1457.81058 · doi:10.1007/JHEP12(2020)172 |
| [36] | Bhardwaj, L.; Hubner, M.; Schäfer-Nameki, S., 1-form symmetries of 4d N = 2 class S theories, SciPost Phys., 11, 096 (2021) · doi:10.21468/SciPostPhys.11.5.096 |
| [37] | K. Costello, D. Gaiotto and J. Yagi, Q-operators are ’t Hooft lines, arXiv:2103.01835 [INSPIRE]. |
| [38] | F. Apruzzi, M. van Beest, D.S.W. Gould and S. Schäfer-Nameki, Holography, 1-form symmetries, and confinement, Phys. Rev. D104 (2021) 066005 [arXiv:2104.12764] [INSPIRE]. |
| [39] | Bhardwaj, L.; Hubner, M.; Schäfer-Nameki, S., Liberating confinement from Lagrangians: 1-form symmetries and lines in 4d N = 1 from 6d N = (2, 0), SciPost Phys., 12, 040 (2022) · doi:10.21468/SciPostPhys.12.1.040 |
| [40] | G. Cuomo, Z. Komargodski and A. Raviv-Moshe, Renormalization group flows on line defects, Phys. Rev. Lett.128 (2022) 021603 [arXiv:2108.01117] [INSPIRE]. |
| [41] | G. Cuomo, Z. Komargodski, M. Mezei and A. Raviv-Moshe, Spin impurities, Wilson lines and semiclassics, JHEP06 (2022) 112 [arXiv:2202.00040] [INSPIRE]. · Zbl 1522.81478 |
| [42] | T.D. Brennan, C. Cordova and T.T. Dumitrescu, Line defect quantum numbers & anomalies, arXiv:2206.15401 [INSPIRE]. |
| [43] | D. Delmastro, J. Gomis, P.-S. Hsin and Z. Komargodski, Anomalies and symmetry fractionalization, arXiv:2206.15118 [INSPIRE]. |
| [44] | Gaiotto, D., N = 2 dualities, JHEP, 08, 034 (2012) · Zbl 1397.81362 · doi:10.1007/JHEP08(2012)034 |
| [45] | D. Gaiotto, G.W. Moore and A. Neitzke, Wall-crossing, Hitchin systems, and the WKB approximation, arXiv:0907.3987 [INSPIRE]. · Zbl 1397.81364 |
| [46] | N. Seiberg and E. Witten, Electric-magnetic duality, monopole condensation, and confinement in N = 2 supersymmetric Yang-Mills theory, Nucl. Phys. B426 (1994) 19 [Erratum ibid.430 (1994) 485] [hep-th/9407087] [INSPIRE]. · Zbl 0996.81511 |
| [47] | Seiberg, N.; Witten, E., Monopoles, duality and chiral symmetry breaking in N = 2 supersymmetric QCD, Nucl. Phys. B, 431, 484 (1994) · Zbl 1020.81911 · doi:10.1016/0550-3213(94)90214-3 |
| [48] | V.V. Fock and A.B. Goncharov, Cluster ensembles, quantization and the dilogarithm, Ann. Sci. École Norm. Supér.42 (2009) 865 [math.AG/0311245] [INSPIRE]. · Zbl 1180.53081 |
| [49] | M. Kontsevich and Y. Soibelman, Stability structures, motivic Donaldson-Thomas invariants and cluster transformations, arXiv:0811.2435 [INSPIRE]. · Zbl 1248.14060 |
| [50] | Dimofte, T.; Gukov, S.; Soibelman, Y., Quantum wall crossing in N = 2 gauge theories, Lett. Math. Phys., 95, 1 (2011) · Zbl 1205.81113 · doi:10.1007/s11005-010-0437-x |
| [51] | I. Affleck and A.W.W. Ludwig, Universal noninteger ‘ground state degeneracy’ in critical quantum systems, Phys. Rev. Lett.67 (1991) 161 [INSPIRE]. · Zbl 0990.81566 |
| [52] | D. Friedan and A. Konechny, On the boundary entropy of one-dimensional quantum systems at low temperature, Phys. Rev. Lett.93 (2004) 030402 [hep-th/0312197] [INSPIRE]. · Zbl 1456.82400 |
| [53] | H. Casini, I. Salazar Landea and G. Torroba, The g-theorem and quantum information theory, JHEP10 (2016) 140 [arXiv:1607.00390] [INSPIRE]. · Zbl 1390.81094 |
| [54] | D. Gaiotto, Boundary F-maximization, arXiv:1403.8052 [INSPIRE]. · Zbl 1452.81163 |
| [55] | K. Jensen and A. O’Bannon, Constraint on defect and boundary renormalization group flows, Phys. Rev. Lett.116 (2016) 091601 [arXiv:1509.02160] [INSPIRE]. |
| [56] | Wang, Y., Surface defect, anomalies and b-extremization, JHEP, 11, 122 (2021) · Zbl 1521.81364 · doi:10.1007/JHEP11(2021)122 |
| [57] | Wang, Y., Defect a-theorem and a-maximization, JHEP, 02, 061 (2022) · Zbl 1522.81579 · doi:10.1007/JHEP02(2022)061 |
| [58] | T. Ekholm and V. Shende, Skeins on branes, arXiv:1901.08027 [INSPIRE]. |
| [59] | H.K. Kim, T.T.Q. Lê and M. Son, SL_2quantum trace in quantum Teichmüller theory via writhe, arXiv:1812.11628 [INSPIRE]. |
| [60] | J. Korinman and A. Quesney, The quantum trace as a quantum non-abelianization map, arXiv:1907.01177. · Zbl 1530.14027 |
| [61] | N.A. Nekrasov and S.L. Shatashvili, Quantization of integrable systems and four dimensional gauge theories, in 16^thInternational Congress on Mathematical Physics, World Scientific, Singapore (2009), p. 265 [arXiv:0908.4052] [INSPIRE]. · Zbl 1214.83049 |
| [62] | Yagi, J., Ω-deformation and quantization, JHEP, 08, 112 (2014) · Zbl 1333.81277 · doi:10.1007/JHEP08(2014)112 |
| [63] | Alday, LF; Gaiotto, D.; Gukov, S.; Tachikawa, Y.; Verlinde, H., Loop and surface operators in N = 2 gauge theory and Liouville modular geometry, JHEP, 01, 113 (2010) · Zbl 1269.81078 · doi:10.1007/JHEP01(2010)113 |
| [64] | D. Xie, Network, cluster coordinates and N = 2 theory I, arXiv:1203.4573 [INSPIRE]. |
| [65] | D. Xie, Network, cluster coordinates and N = 2 theory II: irregular singularity, arXiv:1207.6112 [INSPIRE]. |
| [66] | D. Xie, Higher laminations, webs and N = 2 line operators, arXiv:1304.2390 [INSPIRE]. |
| [67] | N. Saulina, Spectral networks and higher web-like structures, arXiv:1409.2561 [INSPIRE]. |
| [68] | Tachikawa, Y.; Watanabe, N., On skein relations in class S theories, JHEP, 06, 186 (2015) · Zbl 1388.81892 · doi:10.1007/JHEP06(2015)186 |
| [69] | I. Coman, M. Gabella and J. Teschner, Line operators in theories of class , quantized moduli space of flat connections, and Toda field theory, JHEP10 (2015) 143 [arXiv:1505.05898] [INSPIRE]. · Zbl 1388.81797 |
| [70] | Ooguri, H.; Vafa, C., Knot invariants and topological strings, Nucl. Phys. B, 577, 419 (2000) · Zbl 1036.81515 · doi:10.1016/S0550-3213(00)00118-8 |
| [71] | Dimofte, T.; Gaiotto, D.; Gukov, S., Gauge theories labelled by three-manifolds, Commun. Math. Phys., 325, 367 (2014) · Zbl 1292.57012 · doi:10.1007/s00220-013-1863-2 |
| [72] | Gadde, A.; Gukov, S.; Putrov, P., Walls, lines, and spectral dualities in 3d gauge theories, JHEP, 05, 047 (2014) · doi:10.1007/JHEP05(2014)047 |
| [73] | Dimofte, T.; Gaiotto, D.; van der Veen, R., RG domain walls and hybrid triangulations, Adv. Theor. Math. Phys., 19, 137 (2015) · Zbl 1315.81073 · doi:10.4310/ATMP.2015.v19.n1.a2 |
| [74] | S. Chun, S. Gukov and D. Roggenkamp, Junctions of surface operators and categorification of quantum groups, arXiv:1507.06318 [INSPIRE]. · Zbl 1362.81050 |
| [75] | D. Gang, N. Kim, M. Romo and M. Yamazaki, Taming supersymmetric defects in 3d-3d correspondence, J. Phys. A49 (2016) 30LT02 [arXiv:1510.03884] [INSPIRE]. · Zbl 1344.81119 |
| [76] | Gukov, S.; Nawata, S.; Saberi, I.; Stošić, M.; Sułkowski, P., Sequencing BPS spectra, JHEP, 03, 004 (2016) · Zbl 1388.81823 · doi:10.1007/JHEP03(2016)004 |
| [77] | S. Gukov, D. Pei, P. Putrov and C. Vafa, BPS spectra and 3-manifold invariants, J. Knot Theor. Ramifications29 (2020) 2040003 [arXiv:1701.06567] [INSPIRE]. · Zbl 1448.57020 |
| [78] | D. Galakhov and G.W. Moore, Comments on the two-dimensional Landau-Ginzburg approach to link homology, arXiv:1607.04222 [INSPIRE]. |
| [79] | D. Gaiotto, G.W. Moore and A. Neitzke, Spectral networks and snakes, Annales Henri Poincaré15 (2014) 61 [arXiv:1209.0866] [INSPIRE]. · Zbl 1301.81262 |
| [80] | V. Chari and A. Pressley, A guide to quantum groups, Cambridge University Press (1995). · Zbl 0839.17010 |
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