Abstract
We investigate the non-perturbative regimes in the class of non-Abelian theories that have been proposed as an ultraviolet completion of 4-D Quantum Field Theory (QFT) generalizing the kinetic energy operators to an infinite series of higher-order derivatives inspired by string field theory. We prove that, at the non-perturbative level, the physical spectrum of the theory is actually corrected by the “infinite number of derivatives” present in the action. We derive a set of Dyson-Schwinger equations in differential form, for correlation functions till two-points, the solution for which are known in the local theory. We obtain that just like in the local theory, the non-local counterpart displays a mass gap, depending also on the mass scale of non-locality, and show that it is damped in the deep UV asymptotically. We point out some possible implications of our result in particle physics and cosmology and discuss aspects of non-local QCD-like scenarios.
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References
J. Polchinski, String theory. Vol. 1: An introduction to the bosonic string, Cambridge Monographs on Mathematical Physics, Cambridge University Press (2007) [DOI] [INSPIRE].
J. Polchinski, String theory. Vol. 2: Superstring theory and beyond, Cambridge Monographs on Mathematical Physics, Cambridge University Press (2007) [DOI] [INSPIRE].
J. W. Moffat, Finite nonlocal gauge field theory, Phys. Rev. D 41 (1990) 1177 [INSPIRE].
D. Evens, J. W. Moffat, G. Kleppe and R. P. Woodard, Nonlocal regularizations of gauge theories, Phys. Rev. D 43 (1991) 499 [INSPIRE].
E. T. Tomboulis, Superrenormalizable gauge and gravitational theories, hep-th/9702146 [INSPIRE].
J. W. Moffat, Ultraviolet Complete Quantum Field Theory and Gauge Invariance, arXiv:1104.5706 [INSPIRE].
E. T. Tomboulis, Nonlocal and quasilocal field theories, Phys. Rev. D 92 (2015) 125037 [arXiv:1507.00981] [INSPIRE].
G. Kleppe and R. P. Woodard, Nonlocal Yang-Mills, Nucl. Phys. B 388 (1992) 81 [hep-th/9203016] [INSPIRE].
E. Witten, Noncommutative Geometry and String Field Theory, Nucl. Phys. B 268 (1986) 253 [INSPIRE].
V. A. Kostelecky and S. Samuel, On a Nonperturbative Vacuum for the Open Bosonic String, Nucl. Phys. B 336 (1990) 263 [INSPIRE].
V. A. Kostelecky and S. Samuel, The Static Tachyon Potential in the Open Bosonic String Theory, Phys. Lett. B 207 (1988) 169 [INSPIRE].
P. G. O. Freund and M. Olson, Nonarchimedean strings, Phys. Lett. B 199 (1987) 186 [INSPIRE].
P. G. O. Freund and E. Witten, Adelic string amplitudes, Phys. Lett. B 199 (1987) 191 [INSPIRE].
L. Brekke, P. G. O. Freund, M. Olson and E. Witten, Nonarchimedean String Dynamics, Nucl. Phys. B 302 (1988) 365 [INSPIRE].
P. H. Frampton and Y. Okada, Effective scalar field theory of p-adic string, Phys. Rev. D 37 (1988) 3077 [INSPIRE].
T. Biswas, M. Grisaru and W. Siegel, Linear Regge trajectories from worldsheet lattice parton field theory, Nucl. Phys. B 708 (2005) 317 [hep-th/0409089] [INSPIRE].
A. A. Tseytlin, On singularities of spherically symmetric backgrounds in string theory, Phys. Lett. B 363 (1995) 223 [hep-th/9509050] [INSPIRE].
W. Siegel, Stringy gravity at short distances, hep-th/0309093 [INSPIRE].
G. Calcagni and L. Modesto, Nonlocality in string theory, J. Phys. A 47 (2014) 355402 [arXiv:1310.4957] [INSPIRE].
L. Modesto, Super-renormalizable Quantum Gravity, Phys. Rev. D 86 (2012) 044005 [arXiv:1107.2403] [INSPIRE].
L. Modesto, Super-renormalizable Higher-Derivative Quantum Gravity, arXiv:1202.0008 [INSPIRE].
L. Modesto, M. Piva and L. Rachwal, Finite quantum gauge theories, Phys. Rev. D 94 (2016) 025021 [arXiv:1506.06227] [INSPIRE].
L. Modesto, L. Rachwał and I. L. Shapiro, Renormalization group in super-renormalizable quantum gravity, Eur. Phys. J. C 78 (2018) 555 [arXiv:1704.03988] [INSPIRE].
T. Biswas and N. Okada, Towards LHC physics with nonlocal Standard Model, Nucl. Phys. B 898 (2015) 113 [arXiv:1407.3331] [INSPIRE].
Particle Data Group collaboration, Review of Particle Physics, Chin. Phys. C 40 (2016) 100001 [INSPIRE].
A. Ghoshal, A. Mazumdar, N. Okada and D. Villalba, Stability of infinite derivative Abelian Higgs models, Phys. Rev. D 97 (2018) 076011 [arXiv:1709.09222] [INSPIRE].
L. Buoninfante, G. Lambiase and A. Mazumdar, Ghost-free infinite derivative quantum field theory, Nucl. Phys. B 944 (2019) 114646 [arXiv:1805.03559] [INSPIRE].
T. Biswas, E. Gerwick, T. Koivisto and A. Mazumdar, Towards singularity and ghost free theories of gravity, Phys. Rev. Lett. 108 (2012) 031101 [arXiv:1110.5249] [INSPIRE].
B. L. Giacchini and T. de Paula Netto, Effective delta sources and regularity in higher-derivative and ghost-free gravity, JCAP 07 (2019) 013 [arXiv:1809.05907] [INSPIRE].
N. Burzillà, B. L. Giacchini, T. d. P. Netto and L. Modesto, Higher-order regularity in local and nonlocal quantum gravity, Eur. Phys. J. C 81 (2021) 462 [arXiv:2012.11829] [INSPIRE].
T. Biswas, A. Conroy, A. S. Koshelev and A. Mazumdar, Generalized ghost-free quadratic curvature gravity, Class. Quant. Grav. 31 (2014) 015022 [Erratum ibid. 31 (2014) 159501] [arXiv:1308.2319] [INSPIRE].
V. P. Frolov, A. Zelnikov and T. de Paula Netto, Spherical collapse of small masses in the ghost-free gravity, JHEP 06 (2015) 107 [arXiv:1504.00412] [INSPIRE].
V. P. Frolov and A. Zelnikov, Head-on collision of ultrarelativistic particles in ghost-free theories of gravity, Phys. Rev. D 93 (2016) 064048 [arXiv:1509.03336] [INSPIRE].
A. S. Koshelev, J. Marto and A. Mazumdar, Schwarzschild 1/r-singularity is not permissible in ghost free quadratic curvature infinite derivative gravity, Phys. Rev. D 98 (2018) 064023 [arXiv:1803.00309] [INSPIRE].
A. S. Koshelev and A. Mazumdar, Do massive compact objects without event horizon exist in infinite derivative gravity?, Phys. Rev. D 96 (2017) 084069 [arXiv:1707.00273] [INSPIRE].
L. Buoninfante, A. S. Koshelev, G. Lambiase and A. Mazumdar, Classical properties of non-local, ghost- and singularity-free gravity, JCAP 09 (2018) 034 [arXiv:1802.00399] [INSPIRE].
A. S. Cornell, G. Harmsen, G. Lambiase and A. Mazumdar, Rotating metric in nonsingular infinite derivative theories of gravity, Phys. Rev. D 97 (2018) 104006 [arXiv:1710.02162] [INSPIRE].
L. Buoninfante, A. S. Koshelev, G. Lambiase, J. Marto and A. Mazumdar, Conformally-flat, non-singular static metric in infinite derivative gravity, JCAP 06 (2018) 014 [arXiv:1804.08195] [INSPIRE].
L. Buoninfante, G. Harmsen, S. Maheshwari and A. Mazumdar, Nonsingular metric for an electrically charged point-source in ghost-free infinite derivative gravity, Phys. Rev. D 98 (2018) 084009 [arXiv:1804.09624] [INSPIRE].
S. Abel, L. Buoninfante and A. Mazumdar, Nonlocal gravity with worldline inversion symmetry, JHEP 01 (2020) 003 [arXiv:1911.06697] [INSPIRE].
L. Buoninfante, G. Lambiase, Y. Miyashita, W. Takebe and M. Yamaguchi, Generalized ghost-free propagators in nonlocal field theories, Phys. Rev. D 101 (2020) 084019 [arXiv:2001.07830] [INSPIRE].
T. Biswas, A. Mazumdar and W. Siegel, Bouncing universes in string-inspired gravity, JCAP 03 (2006) 009 [hep-th/0508194] [INSPIRE].
T. Biswas, R. Brandenberger, A. Mazumdar and W. Siegel, Non-perturbative Gravity, Hagedorn Bounce & CMB, JCAP 12 (2007) 011 [hep-th/0610274] [INSPIRE].
T. Biswas, T. Koivisto and A. Mazumdar, Towards a resolution of the cosmological singularity in non-local higher derivative theories of gravity, JCAP 11 (2010) 008 [arXiv:1005.0590] [INSPIRE].
T. Biswas, A. S. Koshelev, A. Mazumdar and S. Y. Vernov, Stable bounce and inflation in non-local higher derivative cosmology, JCAP 08 (2012) 024 [arXiv:1206.6374] [INSPIRE].
A. S. Koshelev and S. Y. Vernov, On bouncing solutions in non-local gravity, Phys. Part. Nucl. 43 (2012) 666 [arXiv:1202.1289] [INSPIRE].
A. S. Koshelev, J. Marto and A. Mazumdar, Towards resolution of anisotropic cosmological singularity in infinite derivative gravity, JCAP 02 (2019) 020 [arXiv:1803.07072] [INSPIRE].
A. S. Koshelev, K. Sravan Kumar and P. Vargas Moniz, Effective models of inflation from a nonlocal framework, Phys. Rev. D 96 (2017) 103503 [arXiv:1604.01440] [INSPIRE].
K. Sravan Kumar and L. Modesto, Non-local Starobinsky inflation in the light of future CMB, arXiv:1810.02345 [INSPIRE].
A. S. Koshelev and A. Tokareva, Non-local self-healing of Higgs inflation, Phys. Rev. D 102 (2020) 123518 [arXiv:2006.06641] [INSPIRE].
A. S. Koshelev, K. S. Kumar and A. A. Starobinsky, Analytic infinite derivative gravity, R2-like inflation, quantum gravity and CMB, Int. J. Mod. Phys. D 29 (2020) 2043018 [arXiv:2005.09550] [INSPIRE].
A. S. Koshelev, K. Sravan Kumar, A. Mazumdar and A. A. Starobinsky, Non-Gaussianities and tensor-to-scalar ratio in non-local R2-like inflation, JHEP 06 (2020) 152 [arXiv:2003.00629] [INSPIRE].
F. S. Gama, J. R. Nascimento, A. Y. Petrov and P. J. Porfirio, One-loop effective potential in the nonlocal supersymmetric gauge theory, Phys. Rev. D 96 (2017) 105009 [arXiv:1710.02043] [INSPIRE].
F. S. Gama, J. R. Nascimento and A. Y. Petrov, Supersymmetric gauge theories with higher derivatives and nonlocal terms in the matter sector, Phys. Rev. D 101 (2020) 105018 [arXiv:2004.09299] [INSPIRE].
A. Ghoshal, Scalar dark matter probes the scale of nonlocality, Int. J. Mod. Phys. A 34 (2019) 1950130 [arXiv:1812.02314] [INSPIRE].
L. Buoninfante, A. Ghoshal, G. Lambiase and A. Mazumdar, Transmutation of nonlocal scale in infinite derivative field theories, Phys. Rev. D 99 (2019) 044032 [arXiv:1812.01441] [INSPIRE].
M. Frasca and A. Ghoshal, Mass Gap in Infinite Derivative Non-local Higgs: Dyson-Schwinger Approach, arXiv:2011.10586 [INSPIRE].
A. Ghoshal, A. Mazumdar, N. Okada and D. Villalba, Nonlocal non-Abelian gauge theory: Conformal invariance and β-function, Phys. Rev. D 104 (2021) 015003 [arXiv:2010.15919] [INSPIRE].
M. Frasca, Quantum Yang-Mills field theory, Eur. Phys. J. Plus 132 (2017) 38 [Erratum ibid. 132 (2017) 242] [arXiv:1509.05292] [INSPIRE].
M. Frasca, Mapping a Massless Scalar Field Theory on a Yang-Mills Theory: Classical Case, Mod. Phys. Lett. A 24 (2009) 2425 [arXiv:0903.2357] [INSPIRE].
M. Frasca, Infrared Gluon and Ghost Propagators, Phys. Lett. B 670 (2008) 73 [arXiv:0709.2042] [INSPIRE].
M. Frasca, Scalar field theory in the strong self-interaction limit, Eur. Phys. J. C 74 (2014) 2929 [arXiv:1306.6530] [INSPIRE].
M. Frasca, Spectrum of Yang-Mills theory in 3 and 4 dimensions, Nucl. Part. Phys. Proc. 294-296 (2018) 124 [arXiv:1708.06184] [INSPIRE].
M. Frasca, Differential Dyson-Schwinger equations for quantum chromodynamics, Eur. Phys. J. C 80 (2020) 707 [arXiv:1901.08124] [INSPIRE].
A. V. Smilga, Lectures on quantum chromodynamics, World Scientific, Singapore (2001) [DOI].
C. M. Bender, K. A. Milton and V. M. Savage, Solution of Schwinger-Dyson equations for PT symmetric quantum field theory, Phys. Rev. D 62 (2000) 085001 [hep-th/9907045] [INSPIRE].
T. T. Wu and C. N. Yang, Some Solutions of the Classical Isotopic Gauge Field Equations, published in: Selected Papers (1945–1980) of Chen Ning Yang, pp. 400–405; in H. Mark and S. Fernbach, Properties Of Matter Under Unusual Conditions, pp. 349–345, New York (1969) [PRINT-67-2362] [INSPIRE].
M. E. Peskin and D. V. Schroeder, An Introduction to quantum field theory, Perseus Books Publishing, Reading (1995) [INSPIRE].
T. Kugo and I. Ojima, Manifestly Covariant Canonical Formulation of Yang-Mills Field Theories: Physical State Subsidiary Conditions and Physical S Matrix Unitarity, Phys. Lett. B 73 (1978) 459 [INSPIRE].
T. Kugo and I. Ojima, Local Covariant Operator Formalism of Nonabelian Gauge Theories and Quark Confinement Problem, Prog. Theor. Phys. Suppl. 66 (1979) 1 [INSPIRE].
M. Chaichian and M. Frasca, Condition for confinement in non-Abelian gauge theories, Phys. Lett. B 781 (2018) 33 [arXiv:1801.09873] [INSPIRE].
M. Frasca, A. Ghoshal and N. Okada, Confinement and Renormalization Group Equations in String-inspired Non-local Gauge Theories, arXiv:2106.07629 [INSPIRE].
K. K. Boddy, J. L. Feng, M. Kaplinghat and T. M. P. Tait, Self-Interacting Dark Matter from a Non-Abelian Hidden Sector, Phys. Rev. D 89 (2014) 115017 [arXiv:1402.3629] [INSPIRE].
K. K. Boddy, J. L. Feng, M. Kaplinghat, Y. Shadmi and T. M. P. Tait, Strongly interacting dark matter: Self-interactions and keV lines, Phys. Rev. D 90 (2014) 095016 [arXiv:1408.6532] [INSPIRE].
A. Salvio and A. Strumia, Agravity, JHEP 06 (2014) 080 [arXiv:1403.4226] [INSPIRE].
X. Calmet, R. Casadio, A. Y. Kamenshchik and O. V. Teryaev, Graviton propagator, renormalization scale and black-hole like states, Phys. Lett. B 774 (2017) 332 [arXiv:1708.01485] [INSPIRE].
X. Calmet and B. Latosh, The Spectrum of Quantum Gravity, Phys. Part. Nucl. Lett. 16 (2019) 656 [arXiv:1907.10024] [INSPIRE].
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Frasca, M., Ghoshal, A. Diluted mass gap in strongly coupled non-local Yang-Mills. J. High Energ. Phys. 2021, 226 (2021). https://doi.org/10.1007/JHEP07(2021)226
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DOI: https://doi.org/10.1007/JHEP07(2021)226