Abstract
Building on [1], we uncover new properties of type-B conformal anomalies for Coulomb-branch operators in continuous families of 4D \( \mathcal{N} \) = 2 SCFTs. We study a large class of such anomalies on the Higgs branch, where conformal symmetry is spontaneously broken, and compare them with their counterpart in the CFT phase. In Lagrangian the- ories, the non-perturbative matching of the anomalies can be determined with a weak coupling Feynman diagram computation involving massive multi-loop banana integrals. We extract the part corresponding to the anomalies of interest. Our calculations support the general conjecture that the Coulomb-branch type-B conformal anomalies always match on the Higgs branch when the IR Coulomb-branch chiral ring is empty. In the opposite case, there are anomalies that do not match. An intriguing implication of the mismatch is the existence of a second covariantly constant metric on the conformal manifold (other than the Zamolodchikov metric), which imposes previously unknown restrictions on its holonomy group.
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V. Niarchos, C. Papageorgakis and E. Pomoni, Type-B anomaly matching and the 6D (2, 0) theory, JHEP 04 (2020) 048 [arXiv:1911.05827] [INSPIRE].
G. ’t Hooft, Naturalness, chiral symmetry, and spontaneous chiral symmetry breaking, NATO Sci. Ser. B 59 (1980) 135 [INSPIRE].
S. Deser and A. Schwimmer, Geometric classification of conformal anomalies in arbitrary dimensions, Phys. Lett. B 309 (1993) 279 [hep-th/9302047] [INSPIRE].
A. Schwimmer and S. Theisen, Spontaneous breaking of conformal invariance and trace anomaly matching, Nucl. Phys. B 847 (2011) 590 [arXiv:1011.0696] [INSPIRE].
H. Osborn, Weyl consistency conditions and a local renormalization group equation for general renormalizable field theories, Nucl. Phys. B 363 (1991) 486 [INSPIRE].
H. Osborn and A.C. Petkou, Implications of conformal invariance in field theories for general dimensions, Annals Phys. 231 (1994) 311 [hep-th/9307010] [INSPIRE].
A. Petkou and K. Skenderis, A nonrenormalization theorem for conformal anomalies, Nucl. Phys. B 561 (1999) 100 [hep-th/9906030] [INSPIRE].
E. Gerchkovitz, J. Gomis and Z. Komargodski, Sphere partition functions and the Zamolodchikov metric, JHEP 11 (2014) 001 [arXiv:1405.7271] [INSPIRE].
E. Gerchkovitz, J. Gomis, N. Ishtiaque, A. Karasik, Z. Komargodski and S.S. Pufu, Correlation functions of Coulomb branch operators, JHEP 01 (2017) 103 [arXiv:1602.05971] [INSPIRE].
V. Pestun, Localization of gauge theory on a four-sphere and supersymmetric Wilson loops, Commun. Math. Phys. 313 (2012) 71 [arXiv:0712.2824] [INSPIRE].
L.F. Alday, D. Gaiotto and Y. Tachikawa, Liouville correlation functions from four-dimensional gauge theories, Lett. Math. Phys. 91 (2010) 167 [arXiv:0906.3219] [INSPIRE].
A.B. Zamolodchikov, Irreversibility of the flux of the renormalization group in a 2D field theory, JETP Lett. 43 (1986) 730 [Pisma Zh. Eksp. Teor. Fiz. 43 (1986) 565] [INSPIRE].
D. Kutasov, Geometry on the space of conformal field theories and contact terms, Phys. Lett. B 220 (1989) 153 [INSPIRE].
K. Ranganathan, H. Sonoda and B. Zwiebach, Connections on the state space over conformal field theories, Nucl. Phys. B 414 (1994) 405 [hep-th/9304053] [INSPIRE].
N. Seiberg, Observations on the moduli space of superconformal field theories, Nucl. Phys. B 303 (1988) 286 [INSPIRE].
V. Asnin, On metric geometry of conformal moduli spaces of four-dimensional superconformal theories, JHEP 09 (2010) 012 [arXiv:0912.2529] [INSPIRE].
Z. Komargodski and A. Schwimmer, On renormalization group flows in four dimensions, JHEP 12 (2011) 099 [arXiv:1107.3987] [INSPIRE].
Y. Nakayama, Can we change c in four-dimensional CFTs by exactly marginal deformations?, JHEP 07 (2017) 004 [arXiv:1702.02324] [INSPIRE].
A. Bzowski, P. McFadden and K. Skenderis, Renormalised CFT 3-point functions of scalars, currents and stress tensors, JHEP 11 (2018) 159 [arXiv:1805.12100] [INSPIRE].
A. Schwimmer and S. Theisen, Osborn equation and irrelevant operators, J. Stat. Mech. 1908 (2019) 084011 [arXiv:1902.04473] [INSPIRE].
Y. Tachikawa, N = 2 supersymmetric dynamics for pedestrians, Lecture Notes in Physis volume 890, Springer, Germany (2013) [arXiv:1312.2684] [INSPIRE].
C. Beem, M. Lemos, P. Liendo, L. Rastelli and B.C. van Rees, The \( \mathcal{N} \) = 2 superconformal bootstrap, JHEP 03 (2016) 183 [arXiv:1412.7541] [INSPIRE].
A. Bourget, A. Pini and D. Rodríguez-Gómez, Gauge theories from principally extended disconnected gauge groups, Nucl. Phys. B 940 (2019) 351 [arXiv:1804.01108] [INSPIRE].
P.C. Argyres and M. Martone, Coulomb branches with complex singularities, JHEP 06 (2018) 045 [arXiv:1804.03152] [INSPIRE].
T. Bourton, A. Pini and E. Pomoni, 4d \( \mathcal{N} \) = 3 indices via discrete gauging, JHEP 10 (2018) 131 [arXiv:1804.05396] [INSPIRE].
S. Penati, A. Santambrogio and D. Zanon, More on correlators and contact terms in N = 4 SYM at order g4, Nucl. Phys. B 593 (2001) 651 [hep-th/0005223] [INSPIRE].
L. de la Cruz, Feynman integrals as A-hypergeometric functions, JHEP 12 (2019) 123 [arXiv:1907.00507] [INSPIRE].
S. Weinzierl, The art of computing loop integrals, Fields Inst. Commun. 50 (2007) 345 [hep-ph/0604068] [INSPIRE].
C. Bogner and S. Weinzierl, Periods and Feynman integrals, J. Math. Phys. 50 (2009) 042302 [arXiv:0711.4863] [INSPIRE].
J.L. Bourjaily, Y.-H. He, A.J. Mcleod, M. Von Hippel and M. Wilhelm, Traintracks through Calabi-Yau manifolds: scattering amplitudes beyond elliptic polylogarithms, Phys. Rev. Lett. 121 (2018) 071603 [arXiv:1805.09326] [INSPIRE].
J.L. Bourjaily, A.J. McLeod, M. von Hippel and M. Wilhelm, Bounded collection of Feynman integral Calabi-Yau geometries, Phys. Rev. Lett. 122 (2019) 031601 [arXiv:1810.07689] [INSPIRE].
J. Broedel, C. Duhr, F. Dulat, R. Marzucca, B. Penante and L. Tancredi, An analytic solution for the equal-mass banana graph, JHEP 09 (2019) 112 [arXiv:1907.03787] [INSPIRE].
J.L. Bourjaily, A.J. McLeod, C. Vergu, M. Volk, M. Von Hippel and M. Wilhelm, Embedding Feynman Integral (Calabi-Yau) geometries in weighted projective space, JHEP 01 (2020) 078 [arXiv:1910.01534] [INSPIRE].
R.P. Klausen, Hypergeometric series representations of Feynman integrals by GKZ hypergeometric systems, JHEP 04 (2020) 121 [arXiv:1910.08651] [INSPIRE].
A. Klemm, C. Nega and R. Safari, The l-loop banana amplitude from GKZ systems and relative Calabi-Yau periods, JHEP 04 (2020) 088 [arXiv:1912.06201] [INSPIRE].
M. Hidding, DiffExp, a Mathematica package for computing Feynman integrals in terms of one-dimensional series expansions, arXiv:2006.05510 [INSPIRE].
K. Bönisch, F. Fischbach, A. Klemm, C. Nega and R. Safari, Analytic structure of all loop banana amplitudes, arXiv:2008.10574 [INSPIRE].
S. Laporta and E. Remiddi, Analytic treatment of the two loop equal mass sunrise graph, Nucl. Phys. B 704 (2005) 349 [hep-ph/0406160] [INSPIRE].
O.V. Tarasov, Hypergeometric representation of the two-loop equal mass sunrise diagram, Phys. Lett. B 638 (2006) 195 [hep-ph/0603227] [INSPIRE].
S. Bloch and P. Vanhove, The elliptic dilogarithm for the sunset graph, J. Number Theor. 148 (2015) 328 [arXiv:1309.5865] [INSPIRE].
V. Mitev and E. Pomoni, Exact Bremsstrahlung and effective couplings, JHEP 06 (2016) 078 [arXiv:1511.02217] [INSPIRE].
N. Arkani-Hamed, A.G. Cohen, D.B. Kaplan, A. Karch and L. Motl, Deconstructing (2,0) and little string theories, JHEP 01 (2003) 083 [hep-th/0110146] [INSPIRE].
M. Bershadsky, Z. Kakushadze and C. Vafa, String expansion as large N expansion of gauge theories, Nucl. Phys. B 523 (1998) 59 [hep-th/9803076] [INSPIRE].
M. Bershadsky and A. Johansen, Large N limit of orbifold field theories, Nucl. Phys. B 536 (1998) 141 [hep-th/9803249] [INSPIRE].
G.S. Hall, Covariantly constant tensors and holonomy structure in general relativity, J. Math. Phys. 32 (1991) 181.
J. Gomis, P.-S. Hsin, Z. Komargodski, A. Schwimmer, N. Seiberg and S. Theisen, Anomalies, conformal manifolds, and spheres, JHEP 03 (2016) 022 [arXiv:1509.08511] [INSPIRE].
M. Baggio, V. Niarchos and K. Papadodimas, tt* equations, localization and exact chiral rings in 4d \( \mathcal{N} \) = 2 SCFTs, JHEP 02 (2015) 122 [arXiv:1409.4212] [INSPIRE].
S. Kobayashi and K. Nomizu, Foundations of differential geometry, Wiley, U.S.A. (1963).
A. Besse, Einstein manifolds, Springer, Berlin Germany (2007).
K. Papadodimas, Topological anti-topological fusion in four-dimensional superconformal field theories, JHEP 08 (2010) 118 [arXiv:0910.4963] [INSPIRE].
M. Baggio, V. Niarchos and K. Papadodimas, Aspects of Berry phase in QFT, JHEP 04 (2017) 062 [arXiv:1701.05587] [INSPIRE].
M. Baggio, V. Niarchos and K. Papadodimas, On exact correlation functions in SU(N) \( \mathcal{N} \) = 2 superconformal QCD, JHEP 11 (2015) 198 [arXiv:1508.03077] [INSPIRE].
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Niarchos, V., Papageorgakis, C., Pini, A. et al. (Mis-)matching type-B anomalies on the Higgs branch. J. High Energ. Phys. 2021, 106 (2021). https://doi.org/10.1007/JHEP01(2021)106
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DOI: https://doi.org/10.1007/JHEP01(2021)106