Abstract
In recent work, we demonstrated that the confined-phase spectrum of non-supersymmetric pure Yang-Mills theory coincides with the spectrum of the chiral sector of a two-dimensional conformal field theory in the large-N limit. This was done within the tractable setting in which the gauge theory is compactified on a three-sphere whose radius is small compared to the strong length scale. In this paper, we generalize these observations by demonstrating that similar results continue to hold even when massless adjoint matter fields are introduced. These results hold for both thermal and (−1)F -twisted partition functions, and collectively suggest that the spectra of large-N confining gauge theories are organized by the symmetries of two-dimensional conformal field theories.
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References
G. ’t Hooft, A Planar Diagram Theory for Strong Interactions, Nucl. Phys. B 72 (1974) 461 [INSPIRE].
E. Witten, Baryons in the 1/n Expansion, Nucl. Phys. B 160 (1979) 57 [INSPIRE].
N. Beisert et al., Review of AdS/CFT Integrability: An Overview, Lett. Math. Phys. 99 (2012) 3 [arXiv:1012.3982] [INSPIRE].
G. Basar, A. Cherman, K.R. Dienes and D.A. McGady, 4D-2D equivalence for large-N Yang-Mills theory, Phys. Rev. D 92 (2015) 105029 [arXiv:1507.08666] [INSPIRE].
O. Aharony, J. Marsano, S. Minwalla, K. Papadodimas and M. Van Raamsdonk, A first order deconfinement transition in large-N Yang-Mills theory on a small S 3, Phys. Rev. D 71 (2005) 125018 [hep-th/0502149] [INSPIRE].
O. Aharony, J. Marsano, S. Minwalla, K. Papadodimas and M. Van Raamsdonk, The Hagedorn-deconfinement phase transition in weakly coupled large-N gauge theories, Adv. Theor. Math. Phys. 8 (2004) 603 [hep-th/0310285] [INSPIRE].
B. Sundborg, The Hagedorn transition, deconfinement and N = 4 SYM theory, Nucl. Phys. B 573 (2000) 349 [hep-th/9908001] [INSPIRE].
A.M. Polyakov, Gauge fields and space-time, Int. J. Mod. Phys. A 17S1 (2002) 119 [hep-th/0110196] [INSPIRE].
G. Basar, A. Cherman and D.A. McGady, Bose-Fermi Degeneracies in Large-N Adjoint QCD, JHEP 07 (2015) 016 [arXiv:1409.1617] [INSPIRE].
G. Basar, A. Cherman, D.A. McGady and M. Yamazaki, Casimir energy of confining large-N gauge theories, Phys. Rev. Lett. 114 (2015) 251604 [arXiv:1408.3120] [INSPIRE].
G. Basar, A. Cherman, D.A. McGady and M. Yamazaki, Temperature-reflection symmetry, Phys. Rev. D 91 (2015) 106004 [arXiv:1406.6329] [INSPIRE].
M. Ünsal, Phases of N = ∞ QCD-like gauge theories on S 3 × S 1 and nonperturbative orbifold-orientifold equivalences, Phys. Rev. D 76 (2007) 025015 [hep-th/0703025] [INSPIRE].
A. Armoni, T.D. Cohen and S. Sen, Center symmetry and the Hagedorn spectrum, Phys. Rev. D 91 (2015) 085007 [arXiv:1502.01356] [INSPIRE].
G. Basar, A. Cherman, D. Dorigoni and M. Ünsal, Volume Independence in the Large-N Limit and an Emergent Fermionic Symmetry, Phys. Rev. Lett. 111 (2013) 121601 [arXiv:1306.2960] [INSPIRE].
F. Zuo and Y.-H. Gao, Hagedorn transition and topological entanglement entropy, Nucl. Phys. B 907 (2016) 764 [arXiv:1511.02028] [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].
C. Romelsberger, Counting chiral primaries in N = 1, D = 4 superconformal field theories, Nucl. Phys. B 747 (2006) 329 [hep-th/0510060] [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].
S.S. Razamat, On a modular property of N = 2 superconformal theories in four dimensions, JHEP 10 (2012) 191 [arXiv:1208.5056] [INSPIRE].
C. Cordova and S.-H. Shao, Schur Indices, BPS Particles and Argyres-Douglas Theories, JHEP 01 (2016) 040 [arXiv:1506.00265] [INSPIRE].
J. Bourdier, N. Drukker and J. Felix, The \( \mathcal{N} \) = 2 Schur index from free fermions, JHEP 01 (2016) 167 [arXiv:1510.07041] [INSPIRE].
J. Bourdier, N. Drukker and J. Felix, The exact Schur index of \( \mathcal{N} \) = 4 SYM, JHEP 11 (2015) 210 [arXiv:1507.08659] [INSPIRE].
H.W.J. Bloete, J.L. Cardy and M.P. Nightingale, Conformal Invariance, the Central Charge and Universal Finite Size Amplitudes at Criticality, Phys. Rev. Lett. 56 (1986) 742 [INSPIRE].
L. Di Pietro and Z. Komargodski, Cardy formulae for SUSY theories in d = 4 and d = 6, JHEP 12 (2014) 031 [arXiv:1407.6061] [INSPIRE].
B. Assel, D. Cassani and D. Martelli, Localization on Hopf surfaces, JHEP 08 (2014) 123 [arXiv:1405.5144] [INSPIRE].
B. Assel, D. Cassani and D. Martelli, Supersymmetric counterterms from new minimal supergravity, JHEP 11 (2014) 135 [arXiv:1410.6487] [INSPIRE].
J. Lorenzen and D. Martelli, Comments on the Casimir energy in supersymmetric field theories, JHEP 07 (2015) 001 [arXiv:1412.7463] [INSPIRE].
B. Assel, D. Cassani, L. Di Pietro, Z. Komargodski, J. Lorenzen and D. Martelli, The Casimir Energy in Curved Space and its Supersymmetric Counterpart, JHEP 07 (2015) 043 [arXiv:1503.05537] [INSPIRE].
A.A. Ardehali, J.T. Liu and P. Szepietowski, High-Temperature Expansion of Supersymmetric Partition Functions, JHEP 07 (2015) 113 [arXiv:1502.07737] [INSPIRE].
A.A. Ardehali, J.T. Liu and P. Szepietowski, Central charges from the \( \mathcal{N} \) = 1 superconformal index, Phys. Rev. Lett. 114 (2015) 091603 [arXiv:1411.5028] [INSPIRE].
N. Bobev, M. Bullimore and H.-C. Kim, Supersymmetric Casimir Energy and the Anomaly Polynomial, JHEP 09 (2015) 142 [arXiv:1507.08553] [INSPIRE].
V. Balasubramanian and P. Kraus, A Stress tensor for Anti-de Sitter gravity, Commun. Math. Phys. 208 (1999) 413 [hep-th/9902121] [INSPIRE].
P. Di Francesco, P. Mathieu, and D. Senechal, Conformal Field Theory, Graduate Texts in Contemporary Physics, Springer-Verlag, New York (1997).
D. Ridout and S. Wood, Bosonic Ghosts at c = 2 as a Logarithmic CFT, Lett. Math. Phys. 105 (2015) 279 [arXiv:1408.4185] [INSPIRE].
E. Witten, Spacetime reconstruction, (2001), http://theory.caltech.edu/jhs60/witten/1.html.
B. Sundborg, Stringy gravity, interacting tensionless strings and massless higher spins, Nucl. Phys. Proc. Suppl. 102 (2001) 113 [hep-th/0103247] [INSPIRE].
P. Bouwknegt and K. Schoutens, W symmetry in conformal field theory, Phys. Rept. 223 (1993) 183 [hep-th/9210010] [INSPIRE].
F. Lesage, P. Mathieu, J. Rasmussen and H. Saleur, The \( \widehat{su}{(2)}_{-1/2} \) WZW model and the beta gamma system, Nucl. Phys. B 647 (2002) 363 [hep-th/0207201] [INSPIRE].
G. Anderson and G.W. Moore, Rationality in Conformal Field Theory, Commun. Math. Phys. 117 (1988) 441 [INSPIRE].
C. Vafa, Toward Classification of Conformal Theories, Phys. Lett. B 206 (1988) 421 [INSPIRE].
E. Shaghoulian, Modular forms and a generalized Cardy formula in higher dimensions, arXiv:1508.02728 [INSPIRE].
E. Witten, Analytic Continuation Of Chern-Simons Theory, AMS/IP Stud. Adv. Math. 50 (2011) 347 [arXiv:1001.2933] [INSPIRE].
G. Basar, G.V. Dunne and M. Ünsal, Resurgence theory, ghost-instantons and analytic continuation of path integrals, JHEP 10 (2013) 041 [arXiv:1308.1108] [INSPIRE].
A. Cherman, D. Dorigoni and M. Ünsal, Decoding perturbation theory using resurgence: Stokes phenomena, new saddle points and Lefschetz thimbles, JHEP 10 (2015) 056 [arXiv:1403.1277] [INSPIRE].
A. Behtash, G.V. Dunne, T. Schäfer, T. Sulejmanpasic and M. Ünsal, Complexified path integrals, exact saddles and supersymmetry, Phys. Rev. Lett. 116 (2016) 011601 [arXiv:1510.00978] [INSPIRE].
A. Behtash, G.V. Dunne, T. Schäfer, T. Sulejmanpasic and M. Ünsal, Toward Picard-Lefschetz Theory of Path Integrals, Complex Saddles and Resurgence, arXiv:1510.03435 [INSPIRE].
N. Beisert, On Yangian Symmetry in Planar N = 4 SYM, arXiv:1004.5423 [INSPIRE].
J. Polchinski, String theory. Volume 1: An introduction to the bosonic string, Cambridge University Press (1998)
D. Kutasov and N. Seiberg, Number of degrees of freedom, density of states and tachyons in string theory and CFT, Nucl. Phys. B 358 (1991) 600 [INSPIRE].
K.R. Dienes, Modular invariance, finiteness and misaligned supersymmetry: New constraints on the numbers of physical string states, Nucl. Phys. B 429 (1994) 533 [hep-th/9402006] [INSPIRE].
K.R. Dienes, M. Moshe and R.C. Myers, String theory, misaligned supersymmetry and the supertrace constraints, Phys. Rev. Lett. 74 (1995) 4767 [hep-th/9503055] [INSPIRE].
K.R. Dienes, Solving the hierarchy problem without supersymmetry or extra dimensions: An alternative approach, Nucl. Phys. B 611 (2001) 146 [hep-ph/0104274] [INSPIRE].
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Basar, G., Cherman, A., Dienes, K.R. et al. Modularity and 4D-2D spectral equivalences for large-N gauge theories with adjoint matter. J. High Energ. Phys. 2016, 148 (2016). https://doi.org/10.1007/JHEP06(2016)148
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DOI: https://doi.org/10.1007/JHEP06(2016)148