×

Janus interface in two-dimensional supersymmetric gauge theories. (English) Zbl 1427.81167

Summary: We study the Janus interface, a domain wall characterized by spatially varying couplings, in two-dimensional \(\mathcal{N} = (2, 2)\) supersymmetric gauge theories on the two-sphere. When the variations of the couplings are small enough, SUSY localization in the Janus background gives an analytic continuation of the sphere partition function. This directly demonstrates that the interface entropy is proportional to the quantity known as Calabi’s diastasis, as originally shown by C. Bachas et al. [“Permeable conformal walls and holography”, ibid. 2002, No. 06, Paper No. 27, 33 p. (2002; doi:10.1088/1126-6708/2002/06/027)]. When the variations are not small, we propose that an analytic continuation of the sphere partition function coincides with the Janus partition function. We give a prescription for performing such analytic continuation and computing monodromies. We also point out that the Janus partition function for the equivariant A-twist is precisely the generating function of A-model correlation functions.

MSC:

81T60 Supersymmetric field theories in quantum mechanics
62P35 Applications of statistics to physics
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] Bachas, C.; Boer, J.; Dijkgraaf, R.; Ooguri, H., Permeable conformal walls and holography, JHEP, 06, 027 (2002) · doi:10.1088/1126-6708/2002/06/027
[2] Bak, D.; Gutperle, M.; Hirano, S., A Dilatonic deformation of AdS_5and its field theory dual, JHEP, 05, 072 (2003) · doi:10.1088/1126-6708/2003/05/072
[3] A.B. Clark, D.Z. Freedman, A. Karch and M. Schnabl, Dual of the Janus solution: An interface conformal field theory, Phys. Rev.D 71 (2005) 066003 [hep-th/0407073] [INSPIRE].
[4] Brunner, I.; Roggenkamp, D., Defects and bulk perturbations of boundary Landau-Ginzburg orbifolds, JHEP, 04, 001 (2008) · Zbl 1246.81315 · doi:10.1088/1126-6708/2008/04/001
[5] Brunner, I.; Jockers, H.; Roggenkamp, D., Defects and D-brane Monodromies, Adv. Theor. Math. Phys., 13, 1077 (2009) · Zbl 1267.81266 · doi:10.4310/ATMP.2009.v13.n4.a4
[6] Gaiotto, D., Surface Operators in N = 2 4d Gauge Theories, JHEP, 11, 090 (2012) · Zbl 1397.81363 · doi:10.1007/JHEP11(2012)090
[7] Jockers, H.; Kumar, V.; Lapan, JM; Morrison, DR; Romo, M., Two-Sphere Partition Functions and Gromov-Witten Invariants, Commun. Math. Phys., 325, 1139 (2014) · Zbl 1301.81253 · doi:10.1007/s00220-013-1874-z
[8] Gomis, J.; Lee, S., Exact Kähler Potential from Gauge Theory and Mirror Symmetry, JHEP, 04, 019 (2013) · Zbl 1342.81586 · doi:10.1007/JHEP04(2013)019
[9] Gerchkovitz, E.; Gomis, J.; Komargodski, Z., Sphere Partition Functions and the Zamolodchikov Metric, JHEP, 11, 001 (2014) · Zbl 1333.81171 · doi:10.1007/JHEP11(2014)001
[10] F. Benini and S. Cremonesi, Partition Functions of \(\mathcal{N} \) = (2, 2) Gauge Theories on S2 and Vortices, Commun. Math. Phys. 334 (2015) 1483 [arXiv:1206.2356] [INSPIRE]. · Zbl 1308.81131
[11] N. Doroud, J. Gomis, B. Le Floch and S. Lee, Exact Results in D = 2 Supersymmetric Gauge Theories, JHEP05 (2013) 093 [arXiv:1206.2606] [INSPIRE]. · Zbl 1342.81573
[12] C. Bachas and D. Plencner, Boundary Weyl anomaly of \(\mathcal{N} \) = (2, 2) superconformal models, JHEP03 (2017) 034 [arXiv:1612.06386] [INSPIRE]. · Zbl 1377.81150
[13] S. Sugishita and S. Terashima, Exact Results in Supersymmetric Field Theories on Manifolds with Boundaries, JHEP11 (2013) 021 [arXiv:1308.1973] [INSPIRE]. · Zbl 1342.81620
[14] Honda, D.; Okuda, T., Exact results for boundaries and domain walls in 2d supersymmetric theories, JHEP, 09, 140 (2015) · Zbl 1388.81218 · doi:10.1007/JHEP09(2015)140
[15] K. Hori and M. Romo, Exact Results In Two-Dimensional (2, 2) Supersymmetric Gauge Theories With Boundary, arXiv:1308.2438 [INSPIRE].
[16] C.P. Bachas, I. Brunner, M.R. Douglas and L. Rastelli, Calabi’s diastasis as interface entropy, Phys. Rev.D 90 (2014) 045004 [arXiv:1311.2202] [INSPIRE].
[17] Calabi, E., Isometric imbedding of complex manifolds, Ann. Math., 58, 1 (1953) · Zbl 0051.13103 · doi:10.2307/1969817
[18] S. Cecotti, D. Gaiotto and C. Vafa, tt* geometry in 3 and 4 dimensions, JHEP05 (2014) 055 [arXiv:1312.1008] [INSPIRE]. · Zbl 1333.81163
[19] A.B. Givental, Homological geometry. I. Projective hypersurfaces, Selecta Math.1 (1995) 325 · Zbl 0920.14028
[20] A.B. Givental, Equivariant Gromov — Witten Invariants, alg-geom/9603021.
[21] A.B. Givental, A mirror theorem for toric complete intersections, in Topological field theory, primitive forms and related topics, Progress in Mathematics Series, volume 160, Birkhäuser, Boston Massachusetts U.S.A. (1998), pp. 141-175 [alg-geom/9701016]. · Zbl 0936.14031
[22] C. Closset, S. Cremonesi and D.S. Park, The equivariant A-twist and gauged linear σ-models on the two-sphere, JHEP06 (2015) 076 [arXiv:1504.06308] [INSPIRE]. · Zbl 1388.81713
[23] W. Lerche, C. Vafa and N.P. Warner, Chiral Rings in N = 2 Superconformal Theories, Nucl. Phys.B 324 (1989) 427 [INSPIRE].
[24] A. Recknagel and V. Schomerus, D-branes in Gepner models, Nucl. Phys.B 531 (1998) 185 [hep-th/9712186] [INSPIRE]. · Zbl 0958.81106
[25] N. Seiberg, Naturalness versus supersymmetric nonrenormalization theorems, Phys. Lett.B 318 (1993) 469 [hep-ph/9309335] [INSPIRE].
[26] D. Gaiotto and E. Witten, Janus Configurations, Chern-Simons Couplings, And The theta-Angle in N = 4 Super Yang-Mills Theory, JHEP06 (2010) 097 [arXiv:0804.2907] [INSPIRE]. · Zbl 1290.81065
[27] S. Cecotti and C. Vafa, Topological antitopological fusion, Nucl. Phys.B 367 (1991) 359 [INSPIRE]. · Zbl 1136.81403
[28] C. Closset and S. Cremonesi, Comments on \(\mathcal{N} \) = (2, 2) supersymmetry on two-manifolds, JHEP07 (2014) 075 [arXiv:1404.2636] [INSPIRE]. · Zbl 1333.81164
[29] T. Okuda, Comments on supersymmetric renormalization in two-dimensional curved spacetime, JHEP12 (2017) 081 [arXiv:1705.06118] [INSPIRE]. · Zbl 1383.83220
[30] J. Knapp, M. Romo and E. Scheidegger, Hemisphere Partition Function and Analytic Continuation to the Conifold Point, Commun. Num. Theor. Phys.11 (2017) 73 [arXiv:1602.01382] [INSPIRE]. · Zbl 1397.81159
[31] D. Erkinger and J. Knapp, Hemisphere Partition Function and Monodromy, JHEP05 (2017) 150 [arXiv:1704.00901] [INSPIRE]. · Zbl 1380.81266
[32] R.L. Bryant and P.A. Griffiths, Some observations on the infinitesimal period relations for regular threefolds with trivial canonical bundle, in Arithmetic and geometry, Progress in Mathematics Series, volume 36, Birkhäuser, Boston Massachusetts U.S.A. (1983), pp. 77-102. · Zbl 0543.14005
[33] Strominger, A., Special Geometry, Commun. Math. Phys., 133, 163 (1990) · Zbl 0716.53068 · doi:10.1007/BF02096559
[34] Freed, DS, Special Kähler manifolds, Commun. Math. Phys., 203, 31 (1999) · Zbl 0940.53040 · doi:10.1007/s002200050604
[35] R.P. Horja, Hypergeometric functions and mirror symmetry in toric varieties, math.AG/9912109.
[36] Bonelli, G.; Sciarappa, A.; Tanzini, A.; Vasko, P., Vortex partition functions, wall crossing and equivariant Gromov-Witten invariants, Commun. Math. Phys., 333, 717 (2015) · Zbl 1307.81054 · doi:10.1007/s00220-014-2193-8
[37] Hosono, S., Local mirror symmetry and type IIA monodromy of Calabi-Yau manifolds, Adv. Theor. Math. Phys., 4, 335 (2000) · Zbl 1008.14006 · doi:10.4310/ATMP.2000.v4.n2.a5
[38] Jockers, H., D-brane monodromies from a matrix-factorization perspective, JHEP, 02, 006 (2007) · doi:10.1088/1126-6708/2007/02/006
[39] S. Hosono, Central charges, symplectic forms and hypergeometric series in local mirror symmetry, hep-th/0404043 [INSPIRE]. · Zbl 1114.14025
[40] P. Candelas, X.C. De La Ossa, P.S. Green and L. Parkes, A Pair of Calabi-Yau manifolds as an exactly soluble superconformal theory, Nucl. Phys.B 359 (1991) 21 [AMS/IP Stud. Adv. Math.9 (1998) 31] [INSPIRE]. · Zbl 1098.32506
[41] S. Hosono, A. Klemm, S. Theisen and S.-T. Yau, Mirror symmetry, mirror map and applications to complete intersection Calabi-Yau spaces, Nucl. Phys.B 433 (1995) 501 [hep-th/9406055] [INSPIRE]. · Zbl 1020.32508
[42] J. Gomis and B. Le Floch, M2-brane surface operators and gauge theory dualities in Toda, JHEP04 (2016) 183 [arXiv:1407.1852] [INSPIRE]. · Zbl 1388.81320
[43] N. Hama and K. Hosomichi, Seiberg-Witten Theories on Ellipsoids, JHEP09 (2012) 033 [Addendum JHEP10 (2012) 051] [arXiv:1206.6359] [INSPIRE]. · Zbl 1397.81147
[44] Benini, F.; Zaffaroni, A., A topologically twisted index for three-dimensional supersymmetric theories, JHEP, 07, 127 (2015) · Zbl 1388.81400 · doi:10.1007/JHEP07(2015)127
[45] Witten, E., Topological σ-models, Commun. Math. Phys., 118, 411 (1988) · Zbl 0674.58047 · doi:10.1007/BF01466725
[46] D.R. Morrison and M.R. Plesser, Summing the instantons: Quantum cohomology and mirror symmetry in toric varieties, Nucl. Phys.B 440 (1995) 279 [hep-th/9412236] [INSPIRE]. · Zbl 0908.14014
[47] Ueda, K.; Yoshida, Y., Equivariant A-twisted GLSM and Gromov-Witten invariants of CY 3-folds in Grassmannians, JHEP, 09, 128 (2017) · Zbl 1382.81209 · doi:10.1007/JHEP09(2017)128
[48] B. Kim, J. Oh, K. Ueda and Y. Yoshida, Residue mirror symmetry for Grassmannians, arXiv:1607.08317. · Zbl 1451.14161
[49] A. Gerhardus, H. Jockers and U. Ninad, The Geometry of Gauged Linear sigma model Correlation Functions, Nucl. Phys.B 933 (2018) 65 [arXiv:1803.10253] [INSPIRE]. · Zbl 1395.81157
[50] T. Okuda, in progress.
[51] M. Herbst, K. Hori and D. Page, Phases Of N = 2 Theories In 1 + 1 Dimensions With Boundary, arXiv:0803.2045 [INSPIRE].
[52] M. Dedushenko, Gluing II: Boundary Localization and Gluing Formulas, arXiv:1807.04278 [INSPIRE]. · Zbl 1388.83787
[53] Howe, PS; Papadopoulos, G., N = 2, D = 2 Supergeometry, Class. Quant. Grav., 4, 11 (1987) · Zbl 0609.53055 · doi:10.1088/0264-9381/4/1/005
[54] M.T. Grisaru and M.E. Wehlau, Prepotentials for (2, 2) supergravity, Int. J. Mod. Phys.A 10 (1995) 753 [hep-th/9409043] [INSPIRE]. · Zbl 1044.83545
[55] M.T. Grisaru and M.E. Wehlau, Superspace measures, invariant actions and component projection formulae for (2, 2) supergravity, Nucl. Phys.B 457 (1995) 219 [hep-th/9508139] [INSPIRE]. · Zbl 1004.83539
[56] S.J. Gates Jr., M.T. Grisaru and M.E. Wehlau, A Study of general 2D, N = 2 matter coupled to supergravity in superspace, Nucl. Phys.B 460 (1996) 579 [hep-th/9509021] [INSPIRE]. · Zbl 1003.83516
[57] S.V. Ketov, 2D, N = 2 and N = 4 supergravity and the Liouville theory in superspace, Phys. Lett.B 377 (1996) 48 [hep-th/9602038] [INSPIRE].
[58] S. Shadchin, On F-term contribution to effective action, JHEP08 (2007) 052 [hep-th/0611278] [INSPIRE]. · Zbl 1326.81212
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.