The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects

Argyres, Philip C.; Uensal, Mithat

doi:10.1007/JHEP08(2012)063

Title: The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects

Journal Article · Fri Aug 10 00:00:00 EDT 2012 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/JHEP08(2012)063· OSTI ID:1362077

Argyres, Philip C. ^[1]; Uensal, Mithat ^[2]

Univ. of Cincinnati, OH (United States)
San Francisco State Univ., CA (United States). Dept Physics & Astronomy; SLAC National Accelerator Lab., Menlo Park, CA (United States)

We study the dynamics of four dimensional gauge theories with adjoint fermions for all gauge groups, both in perturbation theory and non-perturbatively, by using circle compactification with periodic boundary conditions for the fermions. There are new gauge phenomena. We show that, to all orders in perturbation theory, many gauge groups are Higgsed by the gauge holonomy around the circle to a product of both abelian and nonabelian gauge group factors. Non-perturbatively there are monopole-instantons with fermion zero modes and two types of monopole-anti-monopole molecules, called bions. One type are magnetic bions which carry net magnetic charge and induce a mass gap for gauge fluctuations. Another type are neutral bions which are magnetically neutral, and their understanding requires a generalization of multi-instanton techniques in quantum mechanics — which we refer to as the Bogomolny-Zinn-Justin (BZJ) prescription — to compactified field theory. The BZJ prescription applied to bion-anti-bion topological molecules predicts a singularity on the positive real axis of the Borel plane (i.e., a divergence from summing large orders in peturbation theory) which is of order N times closer to the origin than the leading 4-d BPST instanton-anti-instanton singularity, where N is the rank of the gauge group. The position of the bion-anti-bion singularity is thus qualitatively similar to that of the 4-d IR renormalon singularity, and we conjecture that they are continuously related as the compactification radius is changed. By making use of transseries and Écalle’s resurgence theory we argue that a non-perturbative continuum definition of a class of field theories which admit semi-classical expansions may be possible.

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Research Organization:: SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), High Energy Physics (HEP)

Grant/Contract Number:: AC02-76SF00515

OSTI ID:: 1362077

Report Number(s):: SLAC-PUB-16996; arXiv:1206.1890

Journal Information:: Journal of High Energy Physics (Online), Vol. 2012, Issue 8; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 127 works

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References (60)

Quantised Singularities in the Electromagnetic Field Dirac, P. A. M. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 133, Issue 821 https://doi.org/10.1098/rspa.1931.0130	journal	September 1931
Hyperasymptotics Berry, M. V.; Howls, C. J. Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences, Vol. 430, Issue 1880, p. 653-668 https://doi.org/10.1098/rspa.1990.0111	journal	September 1990
Renormalons Beneke, M. Physics Reports, Vol. 317, Issue 1-2 https://doi.org/10.1016/S0370-1573(98)00130-6	journal	August 1999
Abelian Duality, Confinement, and Chiral-Symmetry Breaking in a SU(2) QCD-Like Theory Ünsal, Mithat Physical Review Letters, Vol. 100, Issue 3 https://doi.org/10.1103/PhysRevLett.100.032005	journal	January 2008
Gauge theories and magnetic charge Goddard, P.; Nuyts, J.; Olive, D. Nuclear Physics B, Vol. 125, Issue 1 https://doi.org/10.1016/0550-3213(77)90221-8	journal	July 1977
Constituent monopoles through the eyes of fermion zero-modes Bruckmann, Falk; Nógrádi, Dániel; van Baal, Pierre Nuclear Physics B, Vol. 666, Issue 1-2 https://doi.org/10.1016/S0550-3213(03)00531-5	journal	August 2003
The large N limit of four dimensional Yang-Mills field coupled to adjoint fermions on a single site lattice Hietanen, A.; Narayanan, R. Journal of High Energy Physics, Vol. 2010, Issue 1 https://doi.org/10.1007/JHEP01(2010)079	journal	January 2010
Quark confinement and topology of gauge theories Polyakov, A. M. Nuclear Physics B, Vol. 120, Issue 3 https://doi.org/10.1016/0550-3213(77)90086-4	journal	March 1977
Multi-instanton contributions in quantum mechanics Zinn-Justin, J. Nuclear Physics B, Vol. 192, Issue 1 https://doi.org/10.1016/0550-3213(81)90197-8	journal	November 1981
Nonperturbative effects and the large-order behavior of matrix models and topological strings Mariño, Marcos; Schiappa, Ricardo; Weiss, Marlene Communications in Number Theory and Physics, Vol. 2, Issue 2 https://doi.org/10.4310/CNTP.2008.v2.n2.a3	journal	January 2008
Volume independence in large N _c QCD-like gauge theories Kovtun, Pavel; Ünsal, Mithat; Yaffe, Laurence G. Journal of High Energy Physics, Vol. 2007, Issue 06 https://doi.org/10.1088/1126-6708/2007/06/019	journal	June 2007
Large order calculations in gauge theories Bogomolny, E. B.; Fateyev, V. A. Physics Letters B, Vol. 71, Issue 1 https://doi.org/10.1016/0370-2693(77)90748-1	journal	November 1977
Monopole constituents inside SU(n) calorons Kraan, Thomas C.; van Baal, Pierre Physics Letters B, Vol. 435, Issue 3-4 https://doi.org/10.1016/S0370-2693(98)00799-0	journal	September 1998
Constraints on supersymmetry breaking Witten, Edward Nuclear Physics B, Vol. 202, Issue 2 https://doi.org/10.1016/0550-3213(82)90071-2	journal	July 1982
Borel and Stokes Nonperturbative Phenomena in Topological String Theory and c = 1 Matrix Models Pasquetti, Sara; Schiappa, Ricardo Annales Henri Poincaré, Vol. 11, Issue 3 https://doi.org/10.1007/s00023-010-0044-5	journal	June 2010
On the phase transition towards permanent quark confinement 't Hooft, G. Nuclear Physics B, Vol. 138, Issue 1 https://doi.org/10.1016/0550-3213(78)90153-0	journal	June 1978
How instantons solve the U(1) problem 't Hooft, G. Physics Reports, Vol. 142, Issue 6 https://doi.org/10.1016/0370-1573(86)90117-1	journal	September 1986
QCD and instantons at finite temperature Gross, David J.; Pisarski, Robert D.; Yaffe, Laurence G. Reviews of Modern Physics, Vol. 53, Issue 1 https://doi.org/10.1103/RevModPhys.53.43	journal	January 1981
Nonperturbative effects and nonperturbative definitions in matrix models and topological strings Mariño, Marcos Journal of High Energy Physics, Vol. 2008, Issue 12 https://doi.org/10.1088/1126-6708/2008/12/114	journal	December 2008
k-string tension from Eguchi-Kawai reduction Armoni, Adi; Dorigoni, Daniele; Veneziano, Gabriele Journal of High Energy Physics, Vol. 2011, Issue 10 https://doi.org/10.1007/JHEP10(2011)086	journal	October 2011
Geometric engineering of N = 1 quantum field theories Katz, Sheldon; Vafa, Cumrun Nuclear Physics B, Vol. 497, Issue 1-2 https://doi.org/10.1016/S0550-3213(97)00283-6	journal	July 1997
Reduction of Dynamical Degrees of Freedom in the Large- $N$ Gauge Theory Eguchi, Tohru; Kawai, Hikaru Physical Review Letters, Vol. 48, Issue 16 https://doi.org/10.1103/PhysRevLett.48.1063	journal	April 1982
A note on perturbation series in supersymmetric gauge theories Russo, Jorge G. Journal of High Energy Physics, Vol. 2012, Issue 6 https://doi.org/10.1007/JHEP06(2012)038	journal	June 2012
Adjoint fermion zero-modes for SU( N ) calorons Pérez, Margarita García; González-Arroyo, Antonio; Sastre, Alfonso Journal of High Energy Physics, Vol. 2009, Issue 06 https://doi.org/10.1088/1126-6708/2009/06/065	journal	June 2009
Instanton molecular vacuum in N = 1 supersymmetric quantum mechanics Balitsky, I. I.; Yung, A. V. Nuclear Physics B, Vol. 274, Issue 2 https://doi.org/10.1016/0550-3213(86)90295-6	journal	September 1986
Conformality or confinement: (IR)relevance of topological excitations Poppitz, Erich; Ünsal, Mithat Journal of High Energy Physics, Vol. 2009, Issue 09 https://doi.org/10.1088/1126-6708/2009/09/050	journal	September 2009
Seiberg-Witten and “Polyakov-like” magnetic bion confinements are continuously connected Poppitz, Erich; Ünsal, Mithat Journal of High Energy Physics, Vol. 2011, Issue 7 https://doi.org/10.1007/JHEP07(2011)082	journal	July 2011
The Devil's Invention: Asymptotic, Superasymptotic and Hyperasymptotic Series Boyd, John P. Acta Applicandae Mathematicae, Vol. 56, Issue 1, p. 1-98 https://doi.org/10.1023/A:1006145903624	journal	March 1999
Microscopic structure of magnetic bions Anber, Mohamed M.; Poppitz, Erich Journal of High Energy Physics, Vol. 2011, Issue 6 https://doi.org/10.1007/JHEP06(2011)136	journal	June 2011
Calculation of instanton-anti-instanton contributions in quantum mechanics Bogomolny, E. B. Physics Letters B, Vol. 91, Issue 3-4 https://doi.org/10.1016/0370-2693(80)91014-X	journal	April 1980
Exact results in non-supersymmetric large N orientifold field theories Armoni, A.; Shifman, M.; Veneziano, G. Nuclear Physics B, Vol. 667, Issue 1-2 https://doi.org/10.1016/S0550-3213(03)00538-8	journal	September 2003
An L2-Index Theorem for Dirac Operators on S1×R3 Nye, Tom M. W.; Singer, Michael A. Journal of Functional Analysis, Vol. 177, Issue 1 https://doi.org/10.1006/jfan.2000.3648	journal	October 2000
Hyperasymptotics for Integrals with Saddles Berry, M. V.; Howls, C. J. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 434, Issue 1892 https://doi.org/10.1098/rspa.1991.0119	journal	September 1991
Monopoles, affine algebras and the gluino condensate Davies, N. Michael; Hollowood, Timothy J.; Khoze, Valentin V. Journal of Mathematical Physics, Vol. 44, Issue 8 https://doi.org/10.1063/1.1586477	journal	August 2003
Instanton vacuum in supersymmetric QCD Yung, A. V. Nuclear Physics B, Vol. 297, Issue 1 https://doi.org/10.1016/0550-3213(88)90199-X	journal	February 1988
Dynamics of non-integrable phases and gauge symmetry breaking Hosotani, Yutaka Annals of Physics, Vol. 190, Issue 2 https://doi.org/10.1016/0003-4916(89)90015-8	journal	March 1989
Instantons and (super-) symmetry breaking in (2+1) dimensions Affleck, Ian; Harvey, Jeffrey; Witten, Edward Nuclear Physics B, Vol. 206, Issue 3 https://doi.org/10.1016/0550-3213(82)90277-2	journal	October 1982
Anharmonic Oscillator Bender, Carl M.; Wu, Tai Tsun Physical Review, Vol. 184, Issue 5 https://doi.org/10.1103/PhysRev.184.1231	journal	August 1969
Premiers pas en calcul étranger Candelpergher, B.; Nosmas, Jean-Claude; Pham, Frédéric Annales de l’institut Fourier, Vol. 43, Issue 1 https://doi.org/10.5802/aif.1327	journal	January 1993
Index theorem for topological excitations on R ³ × S ¹ and Chern-Simons theory Poppitz, Erich; Ünsal, Mithat Journal of High Energy Physics, Vol. 2009, Issue 03 https://doi.org/10.1088/1126-6708/2009/03/027	journal	March 2009
Collective-coordinate method for quasizero modes Balitsky, I. I.; Yung, A. V. Physics Letters B, Vol. 168, Issue 1-2 https://doi.org/10.1016/0370-2693(86)91471-1	journal	February 1986
Lie Groups and Lie Algebras Tu, Loring W. An Introduction to Manifolds https://doi.org/10.1007/978-1-4419-7400-6_5	book	January 2011
Notes on Lie algebras Tao, Terence Graduate Studies in Mathematics https://doi.org/10.1090/gsm/164/11	book	April 2015
Introduction to lie Algebras and Representation Theory Ledermann, W. Bulletin of the London Mathematical Society, Vol. 6, Issue 2 https://doi.org/10.1112/blms/6.2.237	journal	July 1974
Sphere packings, lattices and groups Rota, Gian-Carlo Advances in Mathematics, Vol. 84, Issue 1 https://doi.org/10.1016/0001-8708(90)90041-k	journal	November 1990
Large Order Calculations in Gauge Theories Bogomolny, E. B.; Fateyev, V. A. Current Physics–Sources and Comments https://doi.org/10.1016/b978-0-444-88597-5.50047-8	book	January 1990
Lie groups and Lie algebras Helgason, Sigurdur Graduate Studies in Mathematics https://doi.org/10.1090/gsm/034/02	book	June 2001
Reflection groups and coxeter groups Bingham, Kouver University of Utah https://doi.org/10.26053/0h-8rtg-5500	text	January 2016
Lie Groups and Lie Algebras Vaughn, Michael T. Introduction to Mathematical Physics https://doi.org/10.1002/9783527618859.ch10	book	May 2007
Lie Groups and Lie Algebras Varadarajan, V. S. Graduate Texts in Mathematics https://doi.org/10.1007/978-1-4612-1126-6_2	book	January 1984
Nonperturbative effects and nonperturbative definitions in matrix models and topological strings Marino, Marcos arXiv https://doi.org/10.48550/arxiv.0805.3033	text	January 2008
Index theorem for topological excitations on R^3 * S^1 and Chern-Simons theory Poppitz, Erich; Unsal, Mithat arXiv https://doi.org/10.48550/arxiv.0812.2085	text	January 2008
The large N limit of four dimensional Yang-Mills field coupled to adjoint fermions on a single site lattice Hietanen, A.; Narayanan, R. arXiv https://doi.org/10.48550/arxiv.0911.2449	text	January 2009
A note on perturbation series in supersymmetric gauge theories Russo, Jorge G. arXiv https://doi.org/10.48550/arxiv.1203.5061	text	January 2012
Monopoles, affine algebras and the gluino condensate Davies, N. Michael; Hollowood, Timothy J.; Khoze, Valentin V. arXiv https://doi.org/10.48550/arxiv.hep-th/0006011	text	January 2000
Exact Results in Non-Supersymmetric Large N Orientifold Field Theories Armoni, A.; Shifman, M.; Veneziano, G. arXiv https://doi.org/10.48550/arxiv.hep-th/0302163	text	January 2003
Constituent monopoles through the eyes of fermion zero-modes Bruckmann, Falk; Nogradi, Daniel; van Baal, Pierre arXiv https://doi.org/10.48550/arxiv.hep-th/0305063	text	January 2003
Volume independence in large Nc QCD-like gauge theories Kovtun, Pavel; Unsal, Mithat; Yaffe, Laurence G. arXiv https://doi.org/10.48550/arxiv.hep-th/0702021	text	January 2007
Geometric Engineering of N=1 Quantum Field Theories Katz, Sheldon; Vafa, Cumrun arXiv https://doi.org/10.48550/arxiv.hep-th/9611090	text	January 1996
Monopole Constituents inside SU(n) Calorons Kraan, Thomas C.; van Baal, Pierre arXiv https://doi.org/10.48550/arxiv.hep-th/9806034	text	January 1998

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