Abstract
We construct the one-dimensional topological sector of \( \mathcal{N} \) = 6 ABJ(M) theory and study its relation with the mass-deformed partition function on S3. Supersymmetric localization provides an exact representation of this partition function as a matrix integral, which interpolates between weak and strong coupling regimes. It has been proposed that correlation functions of dimension-one topological operators should be computed through suitable derivatives with respect to the masses, but a precise proof is still lacking. We present non-trivial evidence for this relation by computing the two-point function at two-loop, successfully matching the matrix model expansion at weak coupling and finite ranks. As a by-product we obtain the two-loop explicit expression for the central charge cT of ABJ(M) theory. Three- and four-point functions up to one-loop confirm the relation as well. Our result points towards the possibility to localize the one-dimensional topological sector of ABJ(M) and may also be useful in the bootstrap program for 3d SCFTs.
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References
J. M. Maldacena, The Large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [INSPIRE].
S. S. Gubser, I. R. Klebanov and A. M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [INSPIRE].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].
C.-M. Chang, S. Minwalla, T. Sharma and X. Yin, ABJ Triality: from Higher Spin Fields to Strings, J. Phys. A 46 (2013) 214009 [arXiv:1207.4485] [INSPIRE].
O. Aharony, O. Bergman, D. L. Jafferis and J. Maldacena, N = 6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals, JHEP 10 (2008) 091 [arXiv:0806.1218] [INSPIRE].
O. Aharony, O. Bergman and D. L. Jafferis, Fractional M2-branes, JHEP 11 (2008) 043 [arXiv:0807.4924] [INSPIRE].
S. El-Showk, M. F. Paulos, D. Poland, S. Rychkov, D. Simmons-Duffin and A. Vichi, Solving the 3D Ising Model with the Conformal Bootstrap, Phys. Rev. D 86 (2012) 025022 [arXiv:1203.6064] [INSPIRE].
V. Pestun et al., Localization techniques in quantum field theories, J. Phys. A 50 (2017) 440301 [arXiv:1608.02952] [INSPIRE].
A. Kapustin, B. Willett and I. Yaakov, Exact Results for Wilson Loops in Superconformal Chern-Simons Theories with Matter, JHEP 03 (2010) 089 [arXiv:0909.4559] [INSPIRE].
S. M. Chester, J. Lee, S. S. Pufu and R. Yacoby, The \( \mathcal{N} \) = 8 superconformal bootstrap in three dimensions, JHEP 09 (2014) 143 [arXiv:1406.4814] [INSPIRE].
S. M. Chester, J. Lee, S. S. Pufu and R. Yacoby, Exact Correlators of BPS Operators from the 3d Superconformal Bootstrap, JHEP 03 (2015) 130 [arXiv:1412.0334] [INSPIRE].
C.-M. Chang, M. Fluder, Y.-H. Lin and Y. Wang, Spheres, Charges, Instantons, and Bootstrap: A Five-Dimensional Odyssey, JHEP 03 (2018) 123 [arXiv:1710.08418] [INSPIRE].
C.-M. Chang and Y.-H. Lin, Carving Out the End of the World or (Superconformal Bootstrap in Six Dimensions), JHEP 08 (2017) 128 [arXiv:1705.05392] [INSPIRE].
M. Baggio, N. Bobev, S. M. Chester, E. Lauria and S. S. Pufu, Decoding a Three-Dimensional Conformal Manifold, JHEP 02 (2018) 062 [arXiv:1712.02698] [INSPIRE].
N. B. Agmon, S. M. Chester and S. S. Pufu, Solving M-theory with the Conformal Bootstrap, JHEP 06 (2018) 159 [arXiv:1711.07343] [INSPIRE].
N. B. Agmon, S. M. Chester and S. S. Pufu, The M-theory Archipelago, JHEP 02 (2020) 010 [arXiv:1907.13222] [INSPIRE].
N. Drukker, S. Giombi, R. Ricci and D. Trancanelli, Supersymmetric Wilson loops on S3, JHEP 05 (2008) 017 [arXiv:0711.3226] [INSPIRE].
V. Pestun, Localization of the four-dimensional N = 4 SYM to a two-sphere and 1/8 BPS Wilson loops, JHEP 12 (2012) 067 [arXiv:0906.0638] [INSPIRE].
S. Giombi and V. Pestun, Correlators of local operators and 1/8 BPS Wilson loops on S2 from 2d YM and matrix models, JHEP 10 (2010) 033 [arXiv:0906.1572] [INSPIRE].
A. Bassetto and L. Griguolo, Two-dimensional QCD, instanton contributions and the perturbative Wu-Mandelstam-Leibbrandt prescription, Phys. Lett. B 443 (1998) 325 [hep-th/9806037] [INSPIRE].
S. Giombi and V. Pestun, Correlators of Wilson Loops and Local Operators from Multi-Matrix Models and Strings in AdS, JHEP 01 (2013) 101 [arXiv:1207.7083] [INSPIRE].
Y. Wang, Taming defects in \( \mathcal{N} \) = 4 super-Yang-Mills, JHEP 08 (2020) 021 [arXiv:2003.11016] [INSPIRE].
C. Beem, W. Peelaers and L. Rastelli, Deformation quantization and superconformal symmetry in three dimensions, Commun. Math. Phys. 354 (2017) 345 [arXiv:1601.05378] [INSPIRE].
M. Dedushenko, S. S. Pufu and R. Yacoby, A one-dimensional theory for Higgs branch operators, JHEP 03 (2018) 138 [arXiv:1610.00740] [INSPIRE].
M. Dedushenko, Y. Fan, S. S. Pufu and R. Yacoby, Coulomb Branch Operators and Mirror Symmetry in Three Dimensions, JHEP 04 (2018) 037 [arXiv:1712.09384] [INSPIRE].
R. Panerai, A. Pittelli and K. Polydorou, Topological Correlators and Surface Defects from Equivariant Cohomology, JHEP 09 (2020) 185 [arXiv:2006.06692] [INSPIRE].
C.-M. Chang, M. Fluder, Y.-H. Lin, S.-H. Shao and Y. Wang, 3d N = 4 Bootstrap and Mirror Symmetry, SciPost Phys. 10 (2021) 097 [arXiv:1910.03600] [INSPIRE].
S. M. Chester, S. S. Pufu and X. Yin, The M-theory S-matrix From ABJM: Beyond 11D Supergravity, JHEP 08 (2018) 115 [arXiv:1804.00949] [INSPIRE].
D. J. Binder, S. M. Chester and S. S. Pufu, AdS4/CFT3 from weak to strong string coupling, JHEP 01 (2020) 034 [arXiv:1906.07195] [INSPIRE].
L. Bianchi, L. Griguolo, M. Preti and D. Seminara, Wilson lines as superconformal defects in ABJM theory: a formula for the emitted radiation, JHEP 10 (2017) 050 [arXiv:1706.06590] [INSPIRE].
A. Kapustin, B. Willett and I. Yaakov, Nonperturbative Tests of Three-Dimensional Dualities, JHEP 10 (2010) 013 [arXiv:1003.5694] [INSPIRE].
D. L. Jafferis, The Exact Superconformal R-Symmetry Extremizes Z, JHEP 05 (2012) 159 [arXiv:1012.3210] [INSPIRE].
N. Hama, K. Hosomichi and S. Lee, Notes on SUSY Gauge Theories on Three-Sphere, JHEP 03 (2011) 127 [arXiv:1012.3512] [INSPIRE].
C. Closset, T. T. Dumitrescu, G. Festuccia, Z. Komargodski and N. Seiberg, Contact Terms, Unitarity, and F-Maximization in Three-Dimensional Superconformal Theories, JHEP 10 (2012) 053 [arXiv:1205.4142] [INSPIRE].
T. Nosaka, K. Shimizu and S. Terashima, Large N behavior of mass deformed ABJM theory, JHEP 03 (2016) 063 [arXiv:1512.00249] [INSPIRE].
T. Nosaka, K. Shimizu and S. Terashima, Mass Deformed ABJM Theory on Three Sphere in Large N limit, JHEP 03 (2017) 121 [arXiv:1608.02654] [INSPIRE].
C. Closset, T. T. Dumitrescu, G. Festuccia and Z. Komargodski, Supersymmetric Field Theories on Three-Manifolds, JHEP 05 (2013) 017 [arXiv:1212.3388] [INSPIRE].
E. Witten, Topological Quantum Field Theory, Commun. Math. Phys. 117 (1988) 353 [INSPIRE].
C. Beem, M. Lemos, P. Liendo, W. Peelaers, L. Rastelli and B.C. van Rees, Infinite Chiral Symmetry in Four Dimensions, Commun. Math. Phys. 336 (2015) 1359 [arXiv:1312.5344] [INSPIRE].
P. Liendo, C. Meneghelli and V. Mitev, On Correlation Functions of BPS Operators in 3d \( \mathcal{N} \) = 6 Superconformal Theories, Commun. Math. Phys. 350 (2017) 387 [arXiv:1512.06072] [INSPIRE].
N. Gorini, L. Griguolo, L. Guerrini, S. Penati, D. Seminara and P. Soresina, in progress.
W. Siegel, Supersymmetric Dimensional Regularization via Dimensional Reduction, Phys. Lett. B 84 (1979) 193 [INSPIRE].
W. Siegel, Inconsistency of Supersymmetric Dimensional Regularization, Phys. Lett. B 94 (1980) 37 [INSPIRE].
M. S. Bianchi, L. Griguolo, A. Mauri, S. Penati and D. Seminara, A matrix model for the latitude Wilson loop in ABJM theory, JHEP 08 (2018) 060 [arXiv:1802.07742] [INSPIRE].
D. J. Binder, S. M. Chester, M. Jerdee and S. S. Pufu, The 3d \( \mathcal{N} \)= 6 bootstrap: from higher spins to strings to membranes, JHEP 05 (2021) 083 [arXiv:2011.05728] [INSPIRE].
V. Cardinali, L. Griguolo, G. Martelloni and D. Seminara, New supersymmetric Wilson loops in ABJ(M) theories, Phys. Lett. B 718 (2012) 615 [arXiv:1209.4032] [INSPIRE].
L. Griguolo, L. Guerrini and I. Yaakov, Localization and Duality for ABJM Latitude Wilson Loops, arXiv:2104.04533 [INSPIRE].
S. Giombi, R. Roiban and A. A. Tseytlin, Half-BPS Wilson loop and AdS2/CFT1, Nucl. Phys. B 922 (2017) 499 [arXiv:1706.00756] [INSPIRE].
P. Liendo, C. Meneghelli and V. Mitev, Bootstrapping the half-BPS line defect, JHEP 10 (2018) 077 [arXiv:1806.01862] [INSPIRE].
S. Giombi and S. Komatsu, Exact Correlators on the Wilson Loop in \( \mathcal{N} \) = 4 SYM: Localization, Defect CFT, and Integrability, JHEP 05 (2018) 109 [Erratum ibid. 11 (2018) 123] [arXiv:1802.05201] [INSPIRE].
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. A 52 (2019) 125401 [arXiv:1811.02369] [INSPIRE].
S. Giombi, J. Jiang and S. Komatsu, Giant Wilson loops and AdS2/dCFT1, JHEP 11 (2020) 064 [arXiv:2005.08890] [INSPIRE].
L. Bianchi, G. Bliard, V. Forini, L. Griguolo and D. Seminara, Analytic bootstrap and Witten diagrams for the ABJM Wilson line as defect CFT1, JHEP 08 (2020) 143 [arXiv:2004.07849] [INSPIRE].
P. Liendo and C. Meneghelli, Bootstrap equations for \( \mathcal{N} \) = 4 SYM with defects, JHEP 01 (2017) 122 [arXiv:1608.05126] [INSPIRE].
D. Young, ABJ(M) Chiral Primary Three-Point Function at Two-loops, JHEP 07 (2014) 120 [arXiv:1404.1117] [INSPIRE].
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Gorini, N., Griguolo, L., Guerrini, L. et al. The topological line of ABJ(M) theory. J. High Energ. Phys. 2021, 91 (2021). https://doi.org/10.1007/JHEP06(2021)091
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DOI: https://doi.org/10.1007/JHEP06(2021)091