Abstract
We initiate the study of a three dimensional disordered supersymmetric field theory. Specifically, we consider a \( \mathcal{N} \) = 2 large N Wess-Zumino like model with cubic superpotential involving couplings drawn from a Gaussian random ensemble. Taking inspiration from analyses of lower dimensional SYK like models we demonstrate that the theory flows to a strongly coupled superconformal fixed point in the infra-red. In particular, we obtain leading large N spectral data and operator product coefficients at the critical point. Moreover, the analytic control accorded by the model allows us to compare our results against those derived in the conformal bootstrap program and demonstrate consistency with general expectations.
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K.G. Wilson and M.E. Fisher, Critical exponents in 3.99 dimensions, Phys. Rev. Lett. 28 (1972) 240 [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].
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 II. c-Minimization and Precise Critical Exponents, J. Stat. Phys. 157 (2014) 869 [arXiv:1403.4545] [INSPIRE].
K. Wilson and J.B. Kogut, The Renormalization group and the epsilon expansion, Phys. Rept. 12 (1974) 75.
E. Brézin and D.J. Wallace, Critical Behavior of a Classical Heisenberg Ferromagnet with Many Degrees of Freedom, Phys. Rev. B 7 (1973) 1967 [INSPIRE].
J. Maldacena and A. Zhiboedov, Constraining conformal field theories with a slightly broken higher spin symmetry, Class. Quant. Grav. 30 (2013) 104003 [arXiv:1204.3882] [INSPIRE].
I.R. Klebanov and A.M. Polyakov, AdS dual of the critical O(N) vector model, Phys. Lett. B 550 (2002) 213 [hep-th/0210114] [INSPIRE].
J.M. Maldacena, The Large N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [hep-th/9711200] [INSPIRE].
S. Sachdev and J. Ye, Gapless spin fluid ground state in a random, quantum Heisenberg magnet, Phys. Rev. Lett. 70 (1993) 3339 [cond-mat/9212030] [INSPIRE].
A. Kitaev, A simple model of quantum holography (part 1), talk at KITP, April 7, 2015, http://online.kitp.ucsb.edu/online/entangled15/kitaev/.
A. Kitaev, A simple model of quantum holography (part 2), talk at KITP, May 27, 2015, http://online.kitp.ucsb.edu/online/entangled15/kitaev2/.
J. Maldacena and D. Stanford, Remarks on the Sachdev-Ye-Kitaev model, Phys. Rev. D 94 (2016) 106002 [arXiv:1604.07818] [INSPIRE].
A. Kitaev and S.J. Suh, The soft mode in the Sachdev-Ye-Kitaev model and its gravity dual, JHEP 05 (2018) 183 [arXiv:1711.08467] [INSPIRE].
J. Maldacena, D. Stanford and Z. Yang, Conformal symmetry and its breaking in two dimensional Nearly Anti-de-Sitter space, PTEP 2016 (2016) 12C104 [arXiv:1606.01857] [INSPIRE].
K. Jensen, Chaos in AdS2 Holography, Phys. Rev. Lett. 117 (2016) 111601 [arXiv:1605.06098] [INSPIRE].
J. Maldacena, S.H. Shenker and D. Stanford, A bound on chaos, JHEP 08 (2016) 106 [arXiv:1503.01409] [INSPIRE].
J.S. Cotler, G. Gur-Ari, M. Hanada, J. Polchinski, P. Saad, S.H. Shenker et al., Black Holes and Random Matrices, JHEP 05 (2017) 118 [Erratum ibid. 09 (2018) 002] [arXiv:1611.04650] [INSPIRE].
J. Maldacena and X.-L. Qi, Eternal traversable wormhole, arXiv:1804.00491 [INSPIRE].
P. Saad, S.H. Shenker and D. Stanford, A semiclassical ramp in SYK and in gravity, arXiv:1806.06840 [INSPIRE].
S. Sachdev, Bekenstein-Hawking Entropy and Strange Metals, Phys. Rev. X 5 (2015) 041025 [arXiv:1506.05111] [INSPIRE].
I. Esterlis, H. Guo, A.A. Patel and S. Sachdev, Large N theory of critical Fermi surfaces, Phys. Rev. B 103 (2021) 235129 [arXiv:2103.08615] [INSPIRE].
E. Witten, An SYK-Like Model Without Disorder, J. Phys. A 52 (2019) 474002 [arXiv:1610.09758] [INSPIRE].
V. Bonzom, R. Gurau, A. Riello and V. Rivasseau, Critical behavior of colored tensor models in the large N limit, Nucl. Phys. B 853 (2011) 174 [arXiv:1105.3122] [INSPIRE].
I.R. Klebanov and G. Tarnopolsky, Uncolored random tensors, melon diagrams, and the Sachdev-Ye-Kitaev models, Phys. Rev. D 95 (2017) 046004 [arXiv:1611.08915] [INSPIRE].
S. Carrozza and A. Tanasa, O(N) Random Tensor Models, Lett. Math. Phys. 106 (2016) 1531 [arXiv:1512.06718] [INSPIRE].
D.J. Gross and V. Rosenhaus, A Generalization of Sachdev-Ye-Kitaev, JHEP 02 (2017) 093 [arXiv:1610.01569] [INSPIRE].
Y. Gu, A. Kitaev, S. Sachdev and G. Tarnopolsky, Notes on the complex Sachdev-Ye-Kitaev model, JHEP 02 (2020) 157 [arXiv:1910.14099] [INSPIRE].
D. Anninos, T. Anous and F. Denef, Disordered Quivers and Cold Horizons, JHEP 12 (2016) 071 [arXiv:1603.00453] [INSPIRE].
W. Fu, D. Gaiotto, J. Maldacena and S. Sachdev, Supersymmetric Sachdev-Ye-Kitaev models, Phys. Rev. D 95 (2017) 026009 [Addendum ibid. 95 (2017) 069904] [arXiv:1610.08917] [INSPIRE].
J. Murugan, D. Stanford and E. Witten, More on Supersymmetric and 2d Analogs of the SYK Model, JHEP 08 (2017) 146 [arXiv:1706.05362] [INSPIRE].
K. Bulycheva, \( \mathcal{N} \) = 2 SYK model in the superspace formalism, JHEP 04 (2018) 036 [arXiv:1801.09006] [INSPIRE].
C. Peng, \( \mathcal{N} \) = (0, 2) SYK, Chaos and Higher-Spins, JHEP 12 (2018) 065 [arXiv:1805.09325] [INSPIRE].
C. Ahn and C. Peng, Chiral Algebras of Two-Dimensional SYK Models, JHEP 07 (2019) 092 [arXiv:1812.05106] [INSPIRE].
C.-M. Chang, S. Colin-Ellerin and M. Rangamani, Supersymmetric Landau-Ginzburg Tensor Models, JHEP 11 (2019) 007 [arXiv:1906.02163] [INSPIRE].
F.K. Popov, Supersymmetric tensor model at large N and small ϵ, Phys. Rev. D 101 (2020) 026020 [arXiv:1907.02440] [INSPIRE].
D. Lettera and A. Vichi, A large-N tensor model with four supercharges, arXiv:2012.11600 [INSPIRE].
O. Aharony, Z. Komargodski and S. Yankielowicz, Disorder in Large-N Theories, JHEP 04 (2016) 013 [arXiv:1509.02547] [INSPIRE].
A. Adams and S. Yaida, Disordered holographic systems: Functional renormalization, Phys. Rev. D 92 (2015) 126008 [arXiv:1102.2892] [INSPIRE].
S.A. Hartnoll and J.E. Santos, Disordered horizons: Holography of randomly disordered fixed points, Phys. Rev. Lett. 112 (2014) 231601 [arXiv:1402.0872] [INSPIRE].
S.A. Hartnoll, D.M. Ramirez and J.E. Santos, Emergent scale invariance of disordered horizons, JHEP 09 (2015) 160 [arXiv:1504.03324] [INSPIRE].
N. Bobev, S. El-Showk, D. Mazac and M.F. Paulos, Bootstrapping the Three-Dimensional Supersymmetric Ising Model, Phys. Rev. Lett. 115 (2015) 051601 [arXiv:1502.04124] [INSPIRE].
N. Bobev, S. El-Showk, D. Mazac and M.F. Paulos, Bootstrapping SCFTs with Four Supercharges, JHEP 08 (2015) 142 [arXiv:1503.02081] [INSPIRE].
A.L. Fitzpatrick, J. Kaplan, D. Poland and D. Simmons-Duffin, The Analytic Bootstrap and AdS Superhorizon Locality, JHEP 12 (2013) 004 [arXiv:1212.3616] [INSPIRE].
Z. Komargodski and A. Zhiboedov, Convexity and Liberation at Large Spin, JHEP 11 (2013) 140 [arXiv:1212.4103] [INSPIRE].
M.S. Costa, V. Goncalves and J. Penedones, Conformal Regge theory, JHEP 12 (2012) 091 [arXiv:1209.4355] [INSPIRE].
R.G. Leigh and M.J. Strassler, Exactly marginal operators and duality in four-dimensional N = 1 supersymmetric gauge theory, Nucl. Phys. B 447 (1995) 95 [hep-th/9503121] [INSPIRE].
C.-M. Chang and X. Yin, Families of Conformal Fixed Points of N = 2 Chern-Simons-Matter Theories, JHEP 05 (2010) 108 [arXiv:1002.0568] [INSPIRE].
D. Green, Z. Komargodski, N. Seiberg, Y. Tachikawa and B. Wecht, Exactly Marginal Deformations and Global Symmetries, JHEP 06 (2010) 106 [arXiv:1005.3546] [INSPIRE].
L.V. Avdeev, S.G. Gorishnii, A.Y. Kamenshchik and S.A. Larin, Four Loop β-function in the Wess-Zumino Model, Phys. Lett. B 117 (1982) 321 [INSPIRE].
I. Jack, D.R.T. Jones and A. Pickering, The soft scalar mass β-function, Phys. Lett. B 432 (1998) 114 [hep-ph/9803405] [INSPIRE].
C.-M. Chang, S. Colin-Ellerin, C. Peng and M. Rangamani, Large N disordered supersymmetric vector models , work in progress.
C. Peng, Vector models and generalized SYK models, JHEP 05 (2017) 129 [arXiv:1704.04223] [INSPIRE].
C.-M. Chang, S. Colin-Ellerin and M. Rangamani, On Melonic Supertensor Models, JHEP 10 (2018) 157 [arXiv:1806.09903] [INSPIRE].
S. Minwalla, Restrictions imposed by superconformal invariance on quantum field theories, Adv. Theor. Math. Phys. 2 (1998) 783 [hep-th/9712074] [INSPIRE].
C. Cordova, T.T. Dumitrescu and K. Intriligator, Multiplets of Superconformal Symmetry in Diverse Dimensions, JHEP 03 (2019) 163 [arXiv:1612.00809] [INSPIRE].
H. Casini, M. Huerta and R.C. Myers, Towards a derivation of holographic entanglement entropy, JHEP 05 (2011) 036 [arXiv:1102.0440] [INSPIRE].
C.-M. Chang, S. Colin-Ellerin, C. Peng and M. Rangamani, Chaos in a strongly coupled disordered 3d QFT, work in progress.
D. Simmons-Duffin, D. Stanford and E. Witten, A spacetime derivation of the Lorentzian OPE inversion formula, JHEP 07 (2018) 085 [arXiv:1711.03816] [INSPIRE].
D. Pappadopulo, S. Rychkov, J. Espin and R. Rattazzi, OPE Convergence in Conformal Field Theory, Phys. Rev. D 86 (2012) 105043 [arXiv:1208.6449] [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].
T. Nishioka and K. Yonekura, On RG Flow of τRR for Supersymmetric Field Theories in Three-Dimensions, JHEP 05 (2013) 165 [arXiv:1303.1522] [INSPIRE].
D. Gang and M. Yamazaki, Expanding 3d \( \mathcal{N} \) = 2 theories around the round sphere, JHEP 02 (2020) 102 [arXiv:1912.09617] [INSPIRE].
D. Li, D. Meltzer and D. Poland, Non-Abelian Binding Energies from the Lightcone Bootstrap, JHEP 02 (2016) 149 [arXiv:1510.07044] [INSPIRE].
A. Kaviraj, K. Sen and A. Sinha, Universal anomalous dimensions at large spin and large twist, JHEP 07 (2015) 026 [arXiv:1504.00772] [INSPIRE].
L.F. Alday, A. Bissi and T. Lukowski, Large spin systematics in CFT, JHEP 11 (2015) 101 [arXiv:1502.07707] [INSPIRE].
P.M. Ferreira, I. Jack and D.R.T. Jones, The Quasiinfrared fixed point at higher loops, Phys. Lett. B 392 (1997) 376 [hep-ph/9610296] [INSPIRE].
P.M. Ferreira and J.A. Gracey, Nonzeta knots in the renormalization of the Wess-Zumino model?, Phys. Lett. B 424 (1998) 85 [hep-th/9712140] [INSPIRE].
S.M. Chester, S. Giombi, L.V. Iliesiu, I.R. Klebanov, S.S. Pufu and R. Yacoby, Accidental Symmetries and the Conformal Bootstrap, JHEP 01 (2016) 110 [arXiv:1507.04424] [INSPIRE].
S.M. Chester, L.V. Iliesiu, S.S. Pufu and R. Yacoby, Bootstrapping O(N) Vector Models with Four Supercharges in 3 ≤ d ≤ 4, JHEP 05 (2016) 103 [arXiv:1511.07552] [INSPIRE].
S.A. Hartnoll and S.P. Kumar, AdS black holes and thermal Yang-Mills correlators, JHEP 12 (2005) 036 [hep-th/0508092] [INSPIRE].
P. Romatschke, Finite-Temperature Conformal Field Theory Results for All Couplings: O(N) Model in 2 + 1 Dimensions, Phys. Rev. Lett. 122 (2019) 231603 [Erratum ibid. 123 (2019) 209901] [arXiv:1904.09995] [INSPIRE].
P. Romatschke, Analytic Transport from Weak to Strong Coupling in the O(N) model, Phys. Rev. D 100 (2019) 054029 [arXiv:1905.09290] [INSPIRE].
M. Mezei and G. Sárosi, Chaos in the butterfly cone, JHEP 01 (2020) 186 [arXiv:1908.03574] [INSPIRE].
S.J. Gates, Y. Hu and S.N.H. Mak, On 1D, N = 4 Supersymmetric SYK-Type Models (I), arXiv:2103.11899 [INSPIRE].
C. Peng, M. Spradlin and A. Volovich, Correlators in the \( \mathcal{N} \) = 2 Supersymmetric SYK Model, JHEP 10 (2017) 202 [arXiv:1706.06078] [INSPIRE].
C. Peng and S. Stanojevic, Soft modes in \( \mathcal{N} \) = 2 SYK model, JHEP 01 (2021) 082 [arXiv:2006.13961] [INSPIRE].
F.A. Dolan and H. Osborn, Conformal Partial Waves: Further Mathematical Results, arXiv:1108.6194 [INSPIRE].
S. Caron-Huot, Analyticity in Spin in Conformal Theories, JHEP 09 (2017) 078 [arXiv:1703.00278] [INSPIRE].
E.I. Buchbinder, S.M. Kuzenko and I.B. Samsonov, Superconformal field theory in three dimensions: Correlation functions of conserved currents, JHEP 06 (2015) 138 [arXiv:1503.04961] [INSPIRE].
A.L. Fitzpatrick, J. Kaplan, Z.U. Khandker, D. Li, D. Poland and D. Simmons-Duffin, Covariant Approaches to Superconformal Blocks, JHEP 08 (2014) 129 [arXiv:1402.1167] [INSPIRE].
Z.U. Khandker, D. Li, D. Poland and D. Simmons-Duffin, \( \mathcal{N} \) = 1 superconformal blocks for general scalar operators, JHEP 08 (2014) 049 [arXiv:1404.5300] [INSPIRE].
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Chang, CM., Colin-Ellerin, S., Peng, C. et al. A 3d disordered superconformal fixed point. J. High Energ. Phys. 2021, 211 (2021). https://doi.org/10.1007/JHEP11(2021)211
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DOI: https://doi.org/10.1007/JHEP11(2021)211