Abstract
We study lower bounds on the minimal distance in theory space between four-dimensional superconformal field theories (SCFTs) connected via broad classes of renormalization group (RG) flows preserving various amounts of supersymmetry (SUSY). For \( \mathcal{N} \) = 1 RG flows, the ultraviolet (UV) and infrared (IR) endpoints of the flow can be parametrically close. On the other hand, for RG flows emanating from a maximally supersymmetric SCFT, the distance to the IR theory cannot be arbitrarily small regardless of the amount of (non-trivial) SUSY preserved along the flow. The case of RG flows from \( \mathcal{N} \) =2 UV SCFTs is more subtle. We argue that for RG flows preserving the full \( \mathcal{N} \) =2 SUSY, there are various obstructions to finding examples with parametrically close UV and IR endpoints. Under reasonable assumptions, these obstructions include: unitarity, known bounds on the c central charge derived from associativity of the operator product expansion, and the central charge bounds of Hofman and Maldacena. On the other hand, for RG flows that break \( \mathcal{N} \) = 2 → \( \mathcal{N} \) = 1, it is possible to find IR fixed points that are parametrically close to the UV ones. In this case, we argue that if the UV SCFT possesses a single stress tensor, then such RG flows excite of order all the degrees of freedom of the UV theory. Furthermore, if the UV theory has some flavor symmetry, we argue that the UV central charges should not be too large relative to certain parameters in the theory.
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References
M.R. Douglas, Spaces of quantum field theories, arXiv:1005.2779 [INSPIRE].
D.M. Hofman and J. Maldacena, Conformal collider physics: energy and charge correlations, JHEP 05 (2008) 012 [arXiv:0803.1467] [INSPIRE].
A. Zhiboedov, On conformal field theories with extremal a/c values, arXiv:1304.6075 [INSPIRE].
D. Poland and D. Simmons-Duffin, Bounds on 4D conformal and superconformal field theories, JHEP 05 (2011) 017 [arXiv:1009.2087] [INSPIRE].
R. Rattazzi, S. Rychkov and A. Vichi, Central charge bounds in 4D conformal field theory, Phys. Rev. D 83 (2011) 046011 [arXiv:1009.2725] [INSPIRE].
F. Caracciolo and V.S. Rychkov, Rigorous limits on the interaction strength in quantum field theory, Phys. Rev. D 81 (2010) 085037 [arXiv:0912.2726] [INSPIRE].
J. Polchinski, Scale and conformal invariance in quantum field theory, Nucl. Phys. B 303 (1988) 226 [INSPIRE].
Y. Nakayama, Higher derivative corrections in holographic Zamolodchikov-Polchinski theorem, Eur. Phys. J. C 72 (2012) 1870 [arXiv:1009.0491] [INSPIRE].
D. Dorigoni and V.S. Rychkov, Scale invariance + unitarity = ⇒ conformal invariance?, arXiv:0910.1087 [INSPIRE].
I. Antoniadis and M. Buican, On R-symmetric fixed points and superconformality, Phys. Rev. D 83 (2011) 105011 [arXiv:1102.2294] [INSPIRE].
M.A. Luty, J. Polchinski and R. Rattazzi, The a-theorem and the asymptotics of 4D quantum field theory, JHEP 01 (2013) 152 [arXiv:1204.5221] [INSPIRE].
J.-F. Fortin, B. Grinstein, C.W. Murphy and A. Stergiou, On limit cycles in supersymmetric theories, Phys. Lett. B 719 (2013) 170 [arXiv:1210.2718] [INSPIRE].
Y. Nakayama, Supercurrent, supervirial and superimprovement, Phys. Rev. D 87 (2013) 085005 [arXiv:1208.4726] [INSPIRE].
J.-F. Fortin, B. Grinstein and A. Stergiou, Limit cycles and conformal invariance, JHEP 01 (2013) 184 [arXiv:1208.3674] [INSPIRE].
Y. Nakayama, A lecture note on scale invariance vs conformal invariance, arXiv:1302.0884 [INSPIRE].
A. Dymarsky, Z. Komargodski, A. Schwimmer and S. Theisen, On scale and conformal invariance in four dimensions, arXiv:1309.2921 [INSPIRE].
K. Farnsworth, M.A. Luty and V. Prelipina, Scale invariance plus unitarity implies conformal invariance in four dimensions, arXiv:1309.4095 [INSPIRE].
K. Yonekura, Perturbative c-theorem in d-dimensions, JHEP 04 (2013) 011 [arXiv:1212.3028] [INSPIRE].
A. Zamolodchikov, Irreversibility of the flux of the renormalization group in a 2D field theory, JETP Lett. 43 (1986) 730 [INSPIRE].
R.C. Myers and A. Sinha, Seeing a c-theorem with holography, Phys. Rev. D 82 (2010) 046006 [arXiv:1006.1263] [INSPIRE].
D.L. Jafferis, I.R. Klebanov, S.S. Pufu and B.R. Safdi, Towards the F-Theorem: N = 2 field theories on the three-sphere, JHEP 06 (2011) 102 [arXiv:1103.1181] [INSPIRE].
R.C. Myers and A. Sinha, Holographic c-theorems in arbitrary dimensions, JHEP 01 (2011) 125 [arXiv:1011.5819] [INSPIRE].
H. Liu and M. Mezei, A refinement of entanglement entropy and the number of degrees of freedom, JHEP 04 (2013) 162 [arXiv:1202.2070] [INSPIRE].
H. Casini and M. Huerta, On the RG running of the entanglement entropy of a circle, Phys. Rev. D 85 (2012) 125016 [arXiv:1202.5650] [INSPIRE].
J.L. Cardy, Is there a c theorem in four-dimensions?, Phys. Lett. B 215 (1988) 749 [INSPIRE].
Z. Komargodski and A. Schwimmer, On renormalization group flows in four dimensions, JHEP 12 (2011) 099 [arXiv:1107.3987] [INSPIRE].
Z. Komargodski, The constraints of conformal symmetry on RG flows, JHEP 07 (2012) 069 [arXiv:1112.4538] [INSPIRE].
H. Elvang et al., On renormalization group flows and the a-theorem in 6d, JHEP 10 (2012) 011 [arXiv:1205.3994] [INSPIRE].
D. Kutasov, Geometry on the space of conformal field theories and contact terms, Phys. Lett. B 220 (1989) 153 [INSPIRE].
M. Buican, A conjectured bound on accidental symmetries, Phys. Rev. D 85 (2012) 025020 [arXiv:1109.3279] [INSPIRE].
M. Bertolini, L. Di Pietro and F. Porri, Holographic R-symmetric flows and the τ U conjecture, JHEP 08 (2013) 071 [arXiv:1304.1481] [INSPIRE].
M. Buican, Non-perturbative constraints on light sparticles from properties of the RG flow, arXiv:1206.3033 [INSPIRE].
K.A. Intriligator, IR free or interacting? A Proposed diagnostic, Nucl. Phys. B 730 (2005) 239 [hep-th/0509085] [INSPIRE].
A. Hook, A test for emergent dynamics, JHEP 07 (2012) 040 [arXiv:1204.4466] [INSPIRE].
G. Vartanov, On the ISS model of dynamical SUSY breaking, Phys. Lett. B 696 (2011) 288 [arXiv:1009.2153] [INSPIRE].
E. Poppitz and M. Ünsal, Chiral gauge dynamics and dynamical supersymmetry breaking, JHEP 07 (2009) 060 [arXiv:0905.0634] [INSPIRE].
E. Gerchkovitz, Constraints on the R-charges of Free Bound States from the Römelsberger Index, arXiv:1311.0487 [INSPIRE].
D. Poland, D. Simmons-Duffin and A. Vichi, Carving out the space of 4D CFTs, JHEP 05 (2012) 110 [arXiv:1109.5176] [INSPIRE].
A. Amariti and K. Intriligator, (Δa) curiosities in some 4D SUSY RG flows, JHEP 11 (2012) 108 [arXiv:1209.4311] [INSPIRE].
Z. Komargodski and N. Seiberg, Comments on supercurrent multiplets, supersymmetric field theories and supergravity, JHEP 07 (2010) 017 [arXiv:1002.2228] [INSPIRE].
Z. Komargodski and N. Seiberg, Comments on the Fayet-Iliopoulos term in field theory and supergravity, JHEP 06 (2009) 007 [arXiv:0904.1159] [INSPIRE].
S. Abel, M. Buican and Z. Komargodski, Mapping anomalous currents in supersymmetric dualities, Phys. Rev. D 84 (2011) 045005 [arXiv:1105.2885] [INSPIRE].
T.T. Dumitrescu and N. Seiberg, Supercurrents and brane currents in diverse dimensions, JHEP 07 (2011) 095 [arXiv:1106.0031] [INSPIRE].
K.A. Intriligator and B. Wecht, The exact superconformal R symmetry maximizes a, Nucl. Phys. B 667 (2003) 183 [hep-th/0304128] [INSPIRE].
D. Erkal and D. Kutasov, a-maximization, global symmetries and RG flows, arXiv:1007.2176 [INSPIRE].
A.D. Shapere and Y. Tachikawa, Central charges of N = 2 superconformal field theories in four dimensions, JHEP 09 (2008) 109 [arXiv:0804.1957] [INSPIRE].
D. Xie and P. Zhao, Central charges and RG flow of strongly-coupled N = 2 theory, JHEP 03 (2013) 006 [arXiv:1301.0210] [INSPIRE].
O. Aharony and Y. Tachikawa, A holographic computation of the central charges of D = 4, N =2 SCFTs, JHEP 01 (2008) 037 [arXiv:0711.4532] [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].
D. Green and D. Shih, Bounds on SCFTs from conformal perturbation theory, JHEP 09 (2012) 026 [arXiv:1203.5129] [INSPIRE].
I. Antoniadis and M. Buican, Goldstinos, supercurrents and metastable SUSY breaking in N =2 supersymmetric gauge theories, JHEP 04 (2011) 101 [arXiv:1005.3012] [INSPIRE].
V. Dobrev and V. Petkova, All positive energy unitary irreducible representations of extended conformal supersymmetry, Phys. Lett. B 162 (1985) 127 [INSPIRE].
F. Dolan and H. Osborn, On short and semi-short representations for four-dimensional superconformal symmetry, Annals Phys. 307 (2003) 41 [hep-th/0209056] [INSPIRE].
S. Minwalla, Restrictions imposed by superconformal invariance on quantum field theories, Adv. Theor. Math. Phys. 2 (1998) 781 [hep-th/9712074] [INSPIRE].
A. Gadde, L. Rastelli, S.S. Razamat and W. Yan, Gauge theories and Macdonald polynomials, Commun. Math. Phys. 319 (2013) 147 [arXiv:1110.3740] [INSPIRE].
N. Seiberg, Supersymmetry and nonperturbative β-functions, Phys. Lett. B 206 (1988) 75 [INSPIRE].
Y. Tachikawa and B. Wecht, Explanation of the central charge ratio 27/32 in four-dimensional renormalization group flows between superconformal theories, Phys. Rev. Lett. 103 (2009) 061601 [arXiv:0906.0965] [INSPIRE].
P.C. Argyres and J.R. Wittig, Infinite coupling duals of N = 2 gauge theories and new rank 1 superconformal field theories, JHEP 01 (2008) 074 [arXiv:0712.2028] [INSPIRE].
J.J. Heckman, Y. Tachikawa, C. Vafa and B. Wecht, N = 1 SCFTs from brane monodromy, JHEP 11 (2010) 132 [arXiv:1009.0017] [INSPIRE].
P.C. Argyres and M.R. Douglas, New phenomena in SU(3) supersymmetric gauge theory, Nucl. Phys. B 448 (1995) 93 [hep-th/9505062] [INSPIRE].
P.C. Argyres, M.R. Plesser, N. Seiberg and E. Witten, New N = 2 superconformal field theories in four-dimensions, Nucl. Phys. B 461 (1996) 71 [hep-th/9511154] [INSPIRE].
T. Eguchi, K. Hori, K. Ito and S.-K. Yang, Study of N = 2 superconformal field theories in four-dimensions, Nucl. Phys. B 471 (1996) 430 [hep-th/9603002] [INSPIRE].
D. Gaiotto, N. Seiberg and Y. Tachikawa, Comments on scaling limits of 4D N = 2 theories, JHEP 01 (2011) 078 [arXiv:1011.4568] [INSPIRE].
S. Giacomelli, Confinement and duality in supersymmetric gauge theories, arXiv:1309.5299 [INSPIRE].
D. Xie, General Argyres-Douglas theory, JHEP 01 (2013) 100 [arXiv:1204.2270] [INSPIRE].
D. Gaiotto, N = 2 dualities, JHEP 08 (2012) 034 [arXiv:0904.2715] [INSPIRE].
K. Papadodimas, Topological anti-topological fusion in four-dimensional superconformal field theories, JHEP 08 (2010) 118 [arXiv:0910.4963] [INSPIRE].
C. Beem, L. Rastelli and B.C. van Rees, The N = 4 superconformal bootstrap, Phys. Rev. Lett. 111 (2013) 071601 [arXiv:1304.1803] [INSPIRE].
J. Maldacena and A. Zhiboedov, Constraining conformal field theories with a higher spin symmetry, J. Phys. A 46 (2013) 214011 [arXiv:1112.1016] [INSPIRE].
V. Alba and K. Diab, Constraining conformal field theories with a higher spin symmetry in D = 4,arXiv:1307.8092 [INSPIRE].
P.C. Argyres and N. Seiberg, S-duality in N = 2 supersymmetric gauge theories, JHEP 12 (2007) 088 [arXiv:0711.0054] [INSPIRE].
J.A. Minahan and D. Nemeschansky, An N = 2 superconformal fixed point with E 6 global symmetry, Nucl. Phys. B 482 (1996) 142 [hep-th/9608047] [INSPIRE].
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Buican, M. Minimal distances between SCFTs. J. High Energ. Phys. 2014, 155 (2014). https://doi.org/10.1007/JHEP01(2014)155
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DOI: https://doi.org/10.1007/JHEP01(2014)155