Abstract
It is an interesting question whether a given infra-red duality between quantum field theories can be explained in terms of other more elementary dualities. For example recently it has been shown that mirror dualities can be obtained by iterative applications of Seiberg-like dualities. In this paper we continue this line of investigation focusing on theories with tensor matter. In such cases one can apply the idea of deconfinement, which consists of trading the tensor matter for extra gauge nodes by means of a suitable elementary duality. This gives an auxiliary dual frame which can then be manipulated with further dualizations, in an iterative procedure eventually yielding an interesting dual description of the original theory. The sequential deconfinement technique has avatars in different areas of mathematical physics, such as the study of hypergeometric and elliptic hypergeometric integral identities or of 2d free field correlators. We discuss various examples in the context 4d \( \mathcal{N} \) = 1 supersymmetric theories, which are related to elliptic hypergeometric integrals. These include a new self-duality involving a quiver theory which exhibits a non-trivial global symmetry enhancement to E6.
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References
N. Seiberg, Electric-magnetic duality in supersymmetric non-Abelian gauge theories, Nucl. Phys. B 435 (1995) 129 [hep-th/9411149] [INSPIRE].
V. Pestun et al., Localization techniques in quantum field theories, J. Phys. A 50 (2017) 440301 [arXiv:1608.02952] [INSPIRE].
C. Hwang, S. Pasquetti and M. Sacchi, Rethinking mirror symmetry as a local duality on fields, arXiv:2110.11362 [INSPIRE].
L. E. Bottini, C. Hwang, S. Pasquetti and M. Sacchi, 4d S-duality wall and SL(2, Z) relations, JHEP 03 (2022) 035 [arXiv:2110.08001] [INSPIRE].
K. A. Intriligator and N. Seiberg, Mirror symmetry in three-dimensional gauge theories, Phys. Lett. B 387 (1996) 513 [hep-th/9607207] [INSPIRE].
C. Hwang, S. Pasquetti and M. Sacchi, 4d mirror-like dualities, JHEP 09 (2020) 047 [arXiv:2002.12897] [INSPIRE].
O. Aharony, IR duality in d = 3 N = 2 supersymmetric USp(2Nc) and U(Nc) gauge theories, Phys. Lett. B 404 (1997) 71 [hep-th/9703215] [INSPIRE].
K. A. Intriligator and P. Pouliot, Exact superpotentials, quantum vacua and duality in supersymmetric SP(Nc) gauge theories, Phys. Lett. B 353 (1995) 471 [hep-th/9505006] [INSPIRE].
C. Csáki, M. Schmaltz and W. Skiba, Confinement in N = 1 SUSY gauge theories and model building tools, Phys. Rev. D 55 (1997) 7840 [hep-th/9612207] [INSPIRE].
M. Berkooz, The dual of supersymmetric SU(2k) with an antisymmetric tensor and composite dualities, Nucl. Phys. B 452 (1995) 513 [hep-th/9505067] [INSPIRE].
P. Pouliot, Duality in SUSY SU(N) with an antisymmetric tensor, Phys. Lett. B 367 (1996) 151 [hep-th/9510148] [INSPIRE].
M. A. Luty, M. Schmaltz and J. Terning, A sequence of duals for Sp(2N) supersymmetric gauge theories with adjoint matter, Phys. Rev. D 54 (1996) 7815 [hep-th/9603034] [INSPIRE].
I. García-Etxebarria, B. Heidenreich and T. Wrase, New N = 1 dualities from orientifold transitions. Part I. Field theory, JHEP 10 (2013) 007 [arXiv:1210.7799] [INSPIRE].
I. García-Etxebarria, B. Heidenreich and T. Wrase, New N = 1 dualities from orientifold transitions. Part II. String theory, JHEP 10 (2013) 006 [arXiv:1307.1701] [INSPIRE].
I. García-Etxebarria, B. Heidenreich, M. Lotito and A. K. Sorout, Deconfining N = 2 SCFTs or the art of brane bending, JHEP 03 (2022) 140 [arXiv:2111.08022] [INSPIRE].
S. Pasquetti and M. Sacchi, From 3d dualities to 2d free field correlators and back, JHEP 11 (2019) 081 [arXiv:1903.10817] [INSPIRE].
S. Pasquetti and M. Sacchi, 3d dualities from 2d free field correlators: recombination and rank stabilization, JHEP 01 (2020) 061 [arXiv:1905.05807] [INSPIRE].
S. Benvenuti, I. Garozzo and G. Lo Monaco, Sequential deconfinement in 3d N = 2 gauge theories, JHEP 07 (2021) 191 [arXiv:2012.09773] [INSPIRE].
S. Benvenuti and G. Lo Monaco, A toolkit for ortho-symplectic dualities, arXiv:2112.12154 [INSPIRE].
K. Nii, 3d deconfinement, product gauge group, Seiberg-Witten and new 3d dualities, JHEP 08 (2016) 123 [arXiv:1603.08550] [INSPIRE].
M. Sacchi, New 2d N = (0, 2) dualities from four dimensions, JHEP 12 (2020) 009 [arXiv:2004.13672] [INSPIRE].
C. Romelsberger, Counting chiral primaries in N = 1, d = 4 superconformal field theories, Nucl. Phys. B 747 (2006) 329 [hep-th/0510060] [INSPIRE].
J. Kinney, J. M. Maldacena, S. Minwalla and S. Raju, An index for 4 dimensional super conformal theories, Commun. Math. Phys. 275 (2007) 209 [hep-th/0510251] [INSPIRE].
F. A. Dolan and H. Osborn, Applications of the superconformal index for protected operators and q-hypergeometric identities to N = 1 dual theories, Nucl. Phys. B 818 (2009) 137 [arXiv:0801.4947] [INSPIRE].
L. Rastelli and S. S. Razamat, The supersymmetric index in four dimensions, J. Phys. A 50 (2017) 443013 [arXiv:1608.02965] [INSPIRE].
V. P. Spiridonov and G. S. Vartanov, Elliptic hypergeometry of supersymmetric dualities, Commun. Math. Phys. 304 (2011) 797 [arXiv:0910.5944] [INSPIRE].
V. P. Spiridonov and G. S. Vartanov, Elliptic hypergeometry of supersymmetric dualities II. Orthogonal groups, knots, and vortices, Commun. Math. Phys. 325 (2014) 421 [arXiv:1107.5788] [INSPIRE].
E. M. Rains, Transformations of elliptic hypergometric integrals, math.QA/0309252.
V. Spiridonov, Theta hypergeometric integrals, St. Petersburg Math. J. 15 (2004) 929 [math.CA/0303205].
H. Dorn and H. J. Otto, Two and three point functions in Liouville theory, Nucl. Phys. B 429 (1994) 375 [hep-th/9403141] [INSPIRE].
A. B. Zamolodchikov and A. B. Zamolodchikov, Structure constants and conformal bootstrap in Liouville field theory, Nucl. Phys. B 477 (1996) 577 [hep-th/9506136] [INSPIRE].
V. A. Fateev and A. V. Litvinov, Multipoint correlation functions in Liouville field theory and minimal Liouville gravity, Theor. Math. Phys. 154 (2008) 454 [arXiv:0707.1664] [INSPIRE].
S. Benvenuti, A tale of exceptional 3d dualities, JHEP 03 (2019) 125 [arXiv:1809.03925] [INSPIRE].
S. Pasquetti, S. S. Razamat, M. Sacchi and G. Zafrir, Rank Q E-string on a torus with flux, SciPost Phys. 8 (2020) 014 [arXiv:1908.03278] [INSPIRE].
C. Hwang, S. S. Razamat, E. Sabag and M. Sacchi, Rank Q E-string on spheres with flux, SciPost Phys. 11 (2021) 044 [arXiv:2103.09149] [INSPIRE].
V. A. Fateev and A. V. Litvinov, Correlation functions in conformal Toda field theory. I, JHEP 11 (2007) 002 [arXiv:0709.3806] [INSPIRE].
V. A. Fateev and A. V. Litvinov, Correlation functions in conformal Toda field theory. II, JHEP 01 (2009) 033 [arXiv:0810.3020] [INSPIRE].
S. Bajeot and S. Benvenuti, S-confinements from deconfinements, arXiv:2201.11049 [INSPIRE].
K. A. Intriligator and B. Wecht, The exact superconformal R symmetry maximizes a, Nucl. Phys. B 667 (2003) 183 [hep-th/0304128] [INSPIRE].
S. Benvenuti and S. Giacomelli, Lagrangians for generalized Argyres-Douglas theories, JHEP 10 (2017) 106 [arXiv:1707.05113] [INSPIRE].
S. Benvenuti and S. Giacomelli, Abelianization and sequential confinement in 2 + 1 dimensions, JHEP 10 (2017) 173 [arXiv:1706.04949] [INSPIRE].
K. A. Intriligator, New RG fixed points and duality in supersymmetric SP(Nc) and SO(Nc) gauge theories, Nucl. Phys. B 448 (1995) 187 [hep-th/9505051] [INSPIRE].
J. F. van Diejen and V. P. Spiridonov, An elliptic Macdonald-Morris conjecture and multiple modular hypergeometric sums, Math. Res. Lett. 7 (2000) 729.
F. Benini, S. Benvenuti and S. Pasquetti, SUSY monopole potentials in 2 + 1 dimensions, JHEP 08 (2017) 086 [arXiv:1703.08460] [INSPIRE].
E. Witten, An SU(2) anomaly, Phys. Lett. B 117 (1982) 324 [INSPIRE].
S. S. Razamat, O. Sela and G. Zafrir, Curious patterns of IR symmetry enhancement, JHEP 10 (2018) 163 [arXiv:1809.00541] [INSPIRE].
C. Hwang, S. Pasquetti and M. Sacchi, Flips, dualities and symmetry enhancements, JHEP 05 (2021) 094 [arXiv:2010.10446] [INSPIRE].
S. S. Razamat and G. Zafrir, E8 orbits of IR dualities, JHEP 11 (2017) 115 [arXiv:1709.06106] [INSPIRE].
S. Benvenuti and S. Giacomelli, Supersymmetric gauge theories with decoupled operators and chiral ring stability, Phys. Rev. Lett. 119 (2017) 251601 [arXiv:1706.02225] [INSPIRE].
C. Beem and A. Gadde, The N = 1 superconformal index for class S fixed points, JHEP 04 (2014) 036 [arXiv:1212.1467] [INSPIRE].
S. Benvenuti, B. Feng, A. Hanany and Y.-H. He, Counting BPS operators in gauge theories: quivers, Syzygies and Plethystics, JHEP 11 (2007) 050 [hep-th/0608050] [INSPIRE].
I. Garozzo, N. Mekareeya, M. Sacchi and G. Zafrir, Symmetry enhancement and duality walls in 5d gauge theories, JHEP 06 (2020) 159 [arXiv:2003.07373] [INSPIRE].
C. Csáki, M. Schmaltz, W. Skiba and J. Terning, Selfdual N = 1 SUSY gauge theories, Phys. Rev. D 56 (1997) 1228 [hep-th/9701191] [INSPIRE].
V. P. Spiridonov and G. S. Vartanov, Superconformal indices for N = 1 theories with multiple duals, Nucl. Phys. B 824 (2010) 192 [arXiv:0811.1909] [INSPIRE].
T. Dimofte and D. Gaiotto, An E7 surprise, JHEP 10 (2012) 129 [arXiv:1209.1404] [INSPIRE].
E. M. Rains, Multivariate quadratic transformations and the interpolation kernel, arXiv:1408.0305.
D. Gaiotto and E. Witten, S-duality of boundary conditions in N = 4 super Yang-Mills theory, Adv. Theor. Math. Phys. 13 (2009) 721 [arXiv:0807.3720] [INSPIRE].
F. Aprile, S. Pasquetti and Y. Zenkevich, Flipping the head of T [SU(N)]: mirror symmetry, spectral duality and monopoles, JHEP 04 (2019) 138 [arXiv:1812.08142] [INSPIRE].
S. Giacomelli, N. Mekareeya and M. Sacchi, New aspects of Argyres-Douglas theories and their dimensional reduction, JHEP 03 (2021) 242 [arXiv:2012.12852] [INSPIRE].
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Bottini, L.E., Hwang, C., Pasquetti, S. et al. Dualities from dualities: the sequential deconfinement technique. J. High Energ. Phys. 2022, 69 (2022). https://doi.org/10.1007/JHEP05(2022)069
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DOI: https://doi.org/10.1007/JHEP05(2022)069