Abstract
We consider a topological coupling between a pseudo-scalar field and a 3- form gauge field in \( \mathcal{N}=1 \) supersymmetric higher derivative 3-form gauge theories in four spacetime dimensions. We show that ghost/tachyon-free higher derivative Lagrangians with the topological coupling can generate various potentials for the pseudo-scalar field by solving the equation of motion for the 3-form gauge field. We give two examples of higher derivative Lagrangians and the corresponding potentials: one is a quartic order term of the field strength and the other is the term which can generate a cosine-type potential of the pseudo-scalar field.
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A. Aurilia and F. Legovini, Extended Systems and Generalized London Equations, Phys. Lett. 67B (1977) 299 [INSPIRE].
A. Aurilia, The Problem of Confinement: From Two-dimensions to Four-dimensions, Phys. Lett. 81B (1979) 203 [INSPIRE].
M. Lüscher, The Secret Long Range Force in Quantum Field Theories With Instantons, Phys. Lett. 78B (1978) 465 [INSPIRE].
A. Aurilia, Y. Takahashi and P.K. Townsend, The U(1) Problem and the Higgs Mechanism in Two-dimensions and Four-dimensions, Phys. Lett. 95B (1980) 265 [INSPIRE].
H. Hata, T. Kugo and N. Ohta, Skew Symmetric Tensor Gauge Field Theory Dynamically Realized in QCD U(1) Channel, Nucl. Phys. B 178 (1981) 527 [INSPIRE].
G. Dvali, Three-form gauging of axion symmetries and gravity, hep-th/0507215 [INSPIRE].
G. Dvali, A vacuum accumulation solution to the strong CP problem, Phys. Rev. D 74 (2006) 025019 [hep-th/0510053] [INSPIRE].
A. Aurilia, H. Nicolai and P.K. Townsend, Hidden Constants: The Theta Parameter of QCD and the Cosmological Constant of N = 8 Supergravity, Nucl. Phys. B 176 (1980) 509 [INSPIRE].
S.W. Hawking, The Cosmological Constant Is Probably Zero, Phys. Lett. 134B (1984) 403 [INSPIRE].
J.D. Brown and C. Teitelboim, Dynamical Neutralization of the Cosmological Constant, Phys. Lett. B 195 (1987) 177 [INSPIRE].
J.D. Brown and C. Teitelboim, Neutralization of the Cosmological Constant by Membrane Creation, Nucl. Phys. B 297 (1988) 787 [INSPIRE].
M.J. Duff, The Cosmological Constant Is Possibly Zero, but the Proof Is Probably Wrong, Phys. Lett. B 226 (1989) 36 [INSPIRE].
M.J. Duncan and L.G. Jensen, Four Forms and the Vanishing of the Cosmological Constant, Nucl. Phys. B 336 (1990) 100 [INSPIRE].
N. Kaloper and L. Sorbo, Where in the String Landscape is Quintessence, Phys. Rev. D 79 (2009) 043528 [arXiv:0810.5346] [INSPIRE].
G. D’Amico, N. Kaloper and A. Lawrence, Strongly Coupled Quintessence, arXiv:1809.05109 [INSPIRE].
N. Kaloper and L. Sorbo, A Natural Framework for Chaotic Inflation, Phys. Rev. Lett. 102 (2009) 121301 [arXiv:0811.1989] [INSPIRE].
N. Kaloper, A. Lawrence and L. Sorbo, An Ignoble Approach to Large Field Inflation, JCAP 03 (2011) 023 [arXiv:1101.0026] [INSPIRE].
F. Marchesano, G. Shiu and A.M. Uranga, F-term Axion Monodromy Inflation, JHEP 09 (2014) 184 [arXiv:1404.3040] [INSPIRE].
N. Kaloper and A. Lawrence, Natural chaotic inflation and ultraviolet sensitivity, Phys. Rev. D 90 (2014) 023506 [arXiv:1404.2912] [INSPIRE].
N. Kaloper and A. Lawrence, London equation for monodromy inflation, Phys. Rev. D 95 (2017) 063526 [arXiv:1607.06105] [INSPIRE].
G. D’Amico, N. Kaloper and A. Lawrence, Monodromy Inflation in the Strong Coupling Regime of the Effective Field Theory, Phys. Rev. Lett. 121 (2018) 091301 [arXiv:1709.07014] [INSPIRE].
S. Ansoldi, A. Aurilia and E. Spallucci, Membrane vacuum as a type-II superconductor, Int. J. Mod. Phys. B 10 (1996) 1695 [hep-th/9511096] [INSPIRE].
K. Hasebe, Higher Dimensional Quantum Hall Effect as A-Class Topological Insulator, Nucl. Phys. B 886 (2014) 952 [arXiv:1403.5066] [INSPIRE].
S.J. Gates Jr., Super p-form gauge superfields, Nucl. Phys. B 184 (1981) 381 [INSPIRE].
S.J. Gates Jr. and W. Siegel, Variant superfield representations, Nucl. Phys. B 187 (1981) 389 [INSPIRE].
I.L. Buchbinder and S.M. Kuzenko, Quantization of the classically equivalent theories in the superspace of simple supergravity and quantum equivalence, Nucl. Phys. B 308 (1988) 162 [INSPIRE].
P. Binetruy, F. Pillon, G. Girardi and R. Grimm, The three form multiplet in supergravity, Nucl. Phys. B 477 (1996) 175 [hep-th/9603181] [INSPIRE].
S.J. Gates, M.T. Grisaru, M. Roček and W. Siegel, Superspace Or One Thousand and One Lessons in Supersymmetry, Front. Phys. 58 (1983) 1 [hep-th/0108200] [INSPIRE].
I.L. Buchbinder and S.M. Kuzenko, Ideas and methods of supersymmetry and supergravity: Or a walk through superspace, IOP, Bristol, U.K., (1998).
P. Binetruy, G. Girardi and R. Grimm, Supergravity couplings: A geometric formulation, Phys. Rept. 343 (2001) 255 [hep-th/0005225] [INSPIRE].
P. Binetruy, M.K. Gaillard and T.R. Taylor, Dynamical supersymmetric breaking and the linear multiplet, Nucl. Phys. B 455 (1995) 97 [hep-th/9504143] [INSPIRE].
P. Binetruy and M.K. Gaillard, S duality constraints on effective potentials for gaugino condensation, Phys. Lett. B 365 (1996) 87 [hep-th/9506207] [INSPIRE].
G.R. Dvali, G. Gabadadze and Z. Kakushadze, BPS domain walls in large N supersymmetric QCD, Nucl. Phys. B 562 (1999) 158 [hep-th/9901032] [INSPIRE].
B.A. Ovrut and D. Waldram, Membranes and three form supergravity, Nucl. Phys. B 506 (1997) 236 [hep-th/9704045] [INSPIRE].
S.M. Kuzenko and G. Tartaglino-Mazzucchelli, Complex three-form supergravity and membranes, JHEP 12 (2017) 005 [arXiv:1710.00535] [INSPIRE].
I. Bandos, F. Farakos, S. Lanza, L. Martucci and D. Sorokin, Three-forms, dualities and membranes in four-dimensional supergravity, JHEP 07 (2018) 028 [arXiv:1803.01405] [INSPIRE].
S.M. Kuzenko and S.A. McCarthy, On the component structure of N = 1 supersymmetric nonlinear electrodynamics, JHEP 05 (2005) 012 [hep-th/0501172] [INSPIRE].
F. Farakos, A. Kehagias, D. Racco and A. Riotto, Scanning of the Supersymmetry Breaking Scale and the Gravitino Mass in Supergravity, JHEP 06 (2016) 120 [arXiv:1605.07631] [INSPIRE].
F. Farakos, S. Lanza, L. Martucci and D. Sorokin, Three-forms in Supergravity and Flux Compactifications, Eur. Phys. J. C 77 (2017) 602 [arXiv:1706.09422] [INSPIRE].
K. Groh, J. Louis and J. Sommerfeld, Duality and Couplings of 3-Form-Multiplets in N = 1 Supersymmetry, JHEP 05 (2013) 001 [arXiv:1212.4639] [INSPIRE].
J. Hartong, M. Hubscher and T. Ortín, The supersymmetric tensor hierarchy of N = 1,d = 4 supergravity, JHEP 06 (2009) 090 [arXiv:0903.0509] [INSPIRE].
K. Becker, M. Becker, W.D. Linch and D. Robbins, Abelian tensor hierarchy in 4D, N = 1 superspace, JHEP 03 (2016) 052 [arXiv:1601.03066] [INSPIRE].
S. Aoki, T. Higaki, Y. Yamada and R. Yokokura, Abelian tensor hierarchy in 4D \( \mathcal{N}=1 \) conformal supergravity, JHEP 09 (2016) 148 [arXiv:1606.04448] [INSPIRE].
E. Dudas, Three-form multiplet and Inflation, JHEP 12 (2014) 014 [arXiv:1407.5688] [INSPIRE].
R. Yokokura, Abelian tensor hierarchy and Chern-Simons actions in 4D \( \mathcal{N}=1 \) conformal supergravity, JHEP 12 (2016) 092 [arXiv:1609.01111] [INSPIRE].
N. Cribiori and S. Lanza, On the dynamical origin of parameters in \( \mathcal{N}=2 \) supersymmetry, Eur. Phys. J. C 79 (2019) 32 [arXiv:1810.11425] [INSPIRE].
E.I. Buchbinder and S.M. Kuzenko, Three-form multiplet and supersymmetry breaking, JHEP 09 (2017) 089 [arXiv:1705.07700] [INSPIRE].
S.M. Kuzenko, Nilpotent \( \mathcal{N}=1 \) tensor multiplet, JHEP 04 (2018) 131 [arXiv:1712.09258] [INSPIRE].
Y. Yamada, U(1) symmetric α-attractors, JHEP 04 (2018) 006 [arXiv:1802.04848] [INSPIRE].
T.L. Curtright and P.G.O. Freund, MASSIVE DUAL FIELDS, Nucl. Phys. B 172 (1980) 413 [INSPIRE].
N. Kaloper and J. Terning, Landscaping the Strong CP Problem, JHEP 03 (2019) 032 [arXiv:1710.01740] [INSPIRE].
S. Franco, D. Galloni, A. Retolaza and A. Uranga, On axion monodromy inflation in warped throats, JHEP 02 (2015) 086 [arXiv:1405.7044] [INSPIRE].
S. Bielleman, L.E. Ibáñez and I. Valenzuela, Minkowski 3-forms, Flux String Vacua, Axion Stability and Naturalness, JHEP 12 (2015) 119 [arXiv:1507.06793] [INSPIRE].
I. Valenzuela, Backreaction Issues in Axion Monodromy and Minkowski 4-forms, JHEP 06 (2017) 098 [arXiv:1611.00394] [INSPIRE].
M. Montero, A.M. Uranga and I. Valenzuela, A Chern-Simons Pandemic, JHEP 07 (2017) 123 [arXiv:1702.06147] [INSPIRE].
M. Nitta and R. Yokokura, Higher derivative three-form gauge theories and their supersymmetric extension, JHEP 10 (2018) 146 [arXiv:1809.03957] [INSPIRE].
M. Ostrogradsky, Mémoires sur les équations différentielles, relatives au problème des isopérimètres, Mem. Acad. St. Petersbourg 6 (1850) 385 [INSPIRE].
R.P. Woodard, Avoiding dark energy with 1/r modifications of gravity, Lect. Notes Phys. 720 (2007) 403 [astro-ph/0601672] [INSPIRE].
F.R. Klinkhamer and G.E. Volovik, Propagating q-field and q-ball solution, Mod. Phys. Lett. A 32 (2017) 1750103 [arXiv:1609.03533] [INSPIRE].
F.R. Klinkhamer and G.E. Volovik, Dark matter from dark energy in q-theory, JETP Lett. 105 (2017) 74 [arXiv:1612.02326] [INSPIRE].
F.R. Klinkhamer and G.E. Volovik, More on cold dark matter from q-theory, arXiv:1612.04235 [INSPIRE].
F.R. Klinkhamer and T. Mistele, Classical stability of higher-derivative q-theory in the four-form-field-strength realization, Int. J. Mod. Phys. A 32 (2017) 1750090 [arXiv:1704.05436] [INSPIRE].
J. Khoury, J.-L. Lehners and B. Ovrut, Supersymmetric P(X, \( \phi \) ) and the Ghost Condensate, Phys. Rev. D 83 (2011) 125031 [arXiv:1012.3748] [INSPIRE].
J. Khoury, J.-L. Lehners and B.A. Ovrut, Supersymmetric Galileons, Phys. Rev. D 84 (2011) 043521 [arXiv:1103.0003] [INSPIRE].
M. Koehn, J.-L. Lehners and B. Ovrut, Ghost condensate in N = 1 supergravity, Phys. Rev. D 87 (2013) 065022 [arXiv:1212.2185] [INSPIRE].
M. Nitta and S. Sasaki, BPS States in Supersymmetric Chiral Models with Higher Derivative Terms, Phys. Rev. D 90 (2014) 105001 [arXiv:1406.7647] [INSPIRE].
I.L. Buchbinder, S. Kuzenko and Z. Yarevskaya, Supersymmetric effective potential: Superfield approach, Nucl. Phys. B 411 (1994) 665 [INSPIRE].
I.L. Buchbinder, S.M. Kuzenko and A.Yu. Petrov, Superfield chiral effective potential, Phys. Lett. B 321 (1994) 372 [INSPIRE].
A.T. Banin, I.L. Buchbinder and N.G. Pletnev, On quantum properties of the four-dimensional generic chiral superfield model, Phys. Rev. D 74 (2006) 045010 [hep-th/0606242] [INSPIRE].
S.M. Kuzenko and S.J. Tyler, The one-loop effective potential of the Wess-Zumino model revisited, JHEP 09 (2014) 135 [arXiv:1407.5270] [INSPIRE].
M. Koehn, J.-L. Lehners and B.A. Ovrut, Higher-Derivative Chiral Superfield Actions Coupled to N = 1 Supergravity, Phys. Rev. D 86 (2012) 085019 [arXiv:1207.3798] [INSPIRE].
F. Farakos and A. Kehagias, Emerging Potentials in Higher-Derivative Gauged Chiral Models Coupled to N = 1 Supergravity, JHEP 11 (2012) 077 [arXiv:1207.4767] [INSPIRE].
J.M. Queiruga, Supersymmetric galileons and auxiliary fields in 2+1 dimensions, Phys. Rev. D 95 (2017) 125001 [arXiv:1612.04727] [INSPIRE].
S. Sasaki, M. Yamaguchi and D. Yokoyama, Supersymmetric DBI inflation, Phys. Lett. B 718 (2012) 1 [arXiv:1205.1353] [INSPIRE].
S. Aoki and Y. Yamada, Inflation in supergravity without Kähler potential, Phys. Rev. D 90 (2014) 127701 [arXiv:1409.4183] [INSPIRE].
S. Aoki and Y. Yamada, Impacts of supersymmetric higher derivative terms on inflation models in supergravity, JCAP 07 (2015) 020 [arXiv:1504.07023] [INSPIRE].
C. Adam, J.M. Queiruga, J. Sanchez-Guillen and A. Wereszczynski, Extended Supersymmetry and BPS solutions in baby Skyrme models, JHEP 05 (2013) 108 [arXiv:1304.0774] [INSPIRE].
C. Adam, J.M. Queiruga, J. Sanchez-Guillen and A. Wereszczynski, N = 1 supersymmetric extension of the baby Skyrme model, Phys. Rev. D 84 (2011) 025008 [arXiv:1105.1168] [INSPIRE].
M. Nitta and S. Sasaki, Classifying BPS States in Supersymmetric Gauge Theories Coupled to Higher Derivative Chiral Models, Phys. Rev. D 91 (2015) 125025 [arXiv:1504.08123] [INSPIRE].
S. Bolognesi and W. Zakrzewski, Baby Skyrme Model, Near-BPS Approximations and Supersymmetric Extensions, Phys. Rev. D 91 (2015) 045034 [arXiv:1407.3140] [INSPIRE].
J.M. Queiruga, Baby Skyrme model and fermionic zero modes, Phys. Rev. D 94 (2016) 065022 [arXiv:1606.02869] [INSPIRE].
J.M. Queiruga, SUSY Chern-Simons ℂℙN and baby Skyrme models and their BPS structures, J. Phys. A 52 (2019) 055202 [arXiv:1807.09612] [INSPIRE].
S.B. Gudnason, M. Nitta and S. Sasaki, A supersymmetric Skyrme model, JHEP 02 (2016) 074 [arXiv:1512.07557] [INSPIRE].
S.B. Gudnason, M. Nitta and S. Sasaki, Topological solitons in the supersymmetric Skyrme model, JHEP 01 (2017) 014 [arXiv:1608.03526] [INSPIRE].
J.M. Queiruga, Skyrme-like models and supersymmetry in 3+1 dimensions, Phys. Rev. D 92 (2015) 105012 [arXiv:1508.06692] [INSPIRE].
J.M. Queiruga and A. Wereszczynski, Non-uniqueness of the supersymmetric extension of the O(3) σ-model, JHEP 11 (2017) 141 [arXiv:1703.07343] [INSPIRE].
M. Eto, T. Fujimori, M. Nitta, K. Ohashi and N. Sakai, Higher Derivative Corrections to Non-Abelian Vortex Effective Theory, Prog. Theor. Phys. 128 (2012) 67 [arXiv:1204.0773] [INSPIRE].
M. Nitta and S. Sasaki, Higher Derivative Corrections to Manifestly Supersymmetric Nonlinear Realizations, Phys. Rev. D 90 (2014) 105002 [arXiv:1408.4210] [INSPIRE].
M. Nitta, S. Sasaki and R. Yokokura, Supersymmetry Breaking in Spatially Modulated Vacua, Phys. Rev. D 96 (2017) 105022 [arXiv:1706.05232] [INSPIRE].
M. Nitta, S. Sasaki and R. Yokokura, Spatially Modulated Vacua in a Lorentz-invariant Scalar Field Theory, Eur. Phys. J. C 78 (2018) 754 [arXiv:1706.02938] [INSPIRE].
F. Farakos, A. Kehagias and A. Riotto, Liberated \( \mathcal{N}= 1 \) supergravity, JHEP 06 (2018) 011 [arXiv:1805.01877] [INSPIRE].
S. Cecotti, S. Ferrara and L. Girardello, Structure of the Scalar Potential in General N = 1 Higher Derivative Supergravity in Four-dimensions, Phys. Lett. B 187 (1987) 321 [INSPIRE].
J. Bagger and A. Galperin, A new Goldstone multiplet for partially broken supersymmetry, Phys. Rev. D 55 (1997) 1091 [hep-th/9608177] [INSPIRE].
S.M. Kuzenko and S. Theisen, Nonlinear selfduality and supersymmetry, Fortsch. Phys. 49 (2001) 273 [hep-th/0007231] [INSPIRE].
S.M. Kuzenko and S.A. McCarthy, Nonlinear selfduality and supergravity, JHEP 02 (2003) 038 [hep-th/0212039] [INSPIRE].
I. Antoniadis, E. Dudas and D.M. Ghilencea, Supersymmetric Models with Higher Dimensional Operators, JHEP 03 (2008) 045 [arXiv:0708.0383] [INSPIRE].
E. Dudas and D.M. Ghilencea, Effective operators in SUSY, superfield constraints and searches for a UV completion, JHEP 06 (2015) 124 [arXiv:1503.08319] [INSPIRE].
T. Fujimori, M. Nitta, K. Ohashi, Y. Yamada and R. Yokokura, Ghost-free vector superfield actions in supersymmetric higher-derivative theories, JHEP 09 (2017) 143 [arXiv:1708.05129] [INSPIRE].
N. Cribiori, F. Farakos, M. Tournoy and A. van Proeyen, Fayet-Iliopoulos terms in supergravity without gauged R-symmetry, JHEP 04 (2018) 032 [arXiv:1712.08601] [INSPIRE].
Y. Aldabergenov, S.V. Ketov and R. Knoops, General couplings of a vector multiplet in N = 1 supergravity with new FI terms, Phys. Lett. B 785 (2018) 284 [arXiv:1806.04290] [INSPIRE].
S.M. Kuzenko, Taking a vector supermultiplet apart: Alternative Fayet-Iliopoulos-type terms, Phys. Lett. B 781 (2018) 723 [arXiv:1801.04794] [INSPIRE].
Y. Aldabergenov and S.V. Ketov, Removing instability of inflation in Polonyi-Starobinsky supergravity by adding FI term, Mod. Phys. Lett. A 91 (2018) 1850032 [arXiv:1711.06789] [INSPIRE].
H. Abe, Y. Aldabergenov, S. Aoki and S.V. Ketov, Massive vector multiplet with Dirac-Born-Infeld and new Fayet-Iliopoulos terms in supergravity, JHEP 09 (2018) 094 [arXiv:1808.00669] [INSPIRE].
J. Wess and J. Bagger, Supersymmetry and supergravity, Princeton University Press, Princeton, U.S.A., (1992).
E. Cremmer, S. Ferrara, L. Girardello and A. Van Proeyen, Yang-Mills Theories with Local Supersymmetry: Lagrangian, Transformation Laws and SuperHiggs Effect, Nucl. Phys. B 212 (1983) 413 [INSPIRE].
T. Kugo and S. Uehara, Conformal and Poincaré Tensor Calculi in N = 1 Supergravity, Nucl. Phys. B 226 (1983) 49 [INSPIRE].
T. Kugo and S. Uehara, Improved Superconformal Gauge Conditions in the N = 1 Supergravity Yang-Mills Matter System, Nucl. Phys. B 222 (1983) 125 [INSPIRE].
T. Kugo and S. Uehara, N = 1 Superconformal Tensor Calculus: Multiplets With External Lorentz Indices and Spinor Derivative Operators, Prog. Theor. Phys. 73 (1985) 235 [INSPIRE].
D. Butter, N = 1 Conformal Superspace in Four Dimensions, Annals Phys. 325 (2010) 1026 [arXiv:0906.4399] [INSPIRE].
T. Kugo, R. Yokokura and K. Yoshioka, Component versus superspace approaches to D = 4, N = 1 conformal supergravity, PTEP 2016 (2016) 073B07 [arXiv:1602.04441] [INSPIRE].
T. Kugo, R. Yokokura and K. Yoshioka, Superspace gauge fixing in Yang-Mills matter-coupled conformal supergravity, PTEP 2016 (2016) 093B03 [arXiv:1606.06515] [INSPIRE].
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Nitta, M., Yokokura, R. Topological couplings in higher derivative extensions of supersymmetric three-form gauge theories. J. High Energ. Phys. 2019, 102 (2019). https://doi.org/10.1007/JHEP05(2019)102
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DOI: https://doi.org/10.1007/JHEP05(2019)102