Abstract
We construct supersymmetric Lifshitz field theories with four real supercharges in a general number of space dimensions. The theories consist of complex bosons and fermions and exhibit a holomorphic structure and non-renormalization properties of the superpotential. We study the theories in a diverse number of space dimensions and for various choices of marginal interactions. We show that there are lines of quantum critical points with an exact Lifshitz scale invariance and a dynamical critical exponent that depends on the coupling constants.
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P. Coleman and A.J. Schofield, Quantum criticality, Nature 433 (2005) 226 [cond-mat/0503002].
S. Sachdev and B. Keimer, Quantum criticality, Phys. Today 64N2 (2011) 29 [arXiv:1102.4628] [INSPIRE].
P. Gegenwart, Q. Si and F. Steglich, Quantum criticality in heavy-fermion metals, Nature Phys. 4 (2008) 186 [arXiv:0712.2045].
S. Sachdev, Quantum phase transitions, Cambridge University Press, Cambridge U.K. (2011).
E. Ardonne, P. Fendley and E. Fradkin, Topological order and conformal quantum critical points, Annals Phys. 310 (2004) 493 [cond-mat/0311466] [INSPIRE].
G. Grinstein, Anisotropic sine-gordon model and infinite-order phase transitions in three dimensions, Phys. Rev. B 23 (1981) 4615.
M. Gurvitch and A.T. Fiory, Resistivity of La1.825 Sr0.175 CuO4 and YBa2 Cu3 O7 to 1100 K: absence of saturation and its implications, Phys. Rev. Lett. 5 (1987) 1337.
O. Trovarelli et al., bRh2 Si2 : pronounced non-Fermi-liquid effects above a low-lying magnetic phase transition, Phys. Rev. Lett. 85 (2000) 626.
J.A.N. Bruin, H. Sakai, R.S. Perry and A. P. Mackenzie, Similarity of scattering rates in metals showing T-linear resistivity, Science 339 (2013) 804.
R.M. Hornreich, M. Luban and S. Shtrikman, Critical behavior at the onset of xk-space instability on the λ line, Phys. Rev. Lett. 35 (1975) 1678 [INSPIRE].
N. Seiberg, Naturalness versus supersymmetric nonrenormalization theorems, Phys. Lett. B 318 (1993) 469 [hep-ph/9309335] [INSPIRE].
M.T. Grisaru, W. Siegel and M. Roček, Improved methods for supergraphs, Nucl. Phys. B 159 (1979) 429 [INSPIRE].
W. Xue, Non-relativistic supersymmetry, arXiv:1008.5102 [INSPIRE].
M. Gomes, J.R. Nascimento, A.Yu. Petrov and A.J. da Silva, Hořava-Lifshitz-like extensions of supersymmetric theories, Phys. Rev. D 90 (2014) 125022 [arXiv:1408.6499] [INSPIRE].
A. Meyer, Y. Oz and A. Raviv-Moshe, On non-relativistic supersymmetry and its spontaneous breaking, JHEP 06 (2017) 128 [arXiv:1703.04740] [INSPIRE].
D. Redigolo, On Lorentz-violating supersymmetric quantum field theories, Phys. Rev. D 85 (2012) 085009 [arXiv:1106.2035] [INSPIRE].
M. Gomes, J. Queiruga and A.J. da Silva, Lorentz breaking supersymmetry and Hǒrava-Lifshitz-like models, Phys. Rev. D 92 (2015) 025050 [arXiv:1506.01331] [INSPIRE].
E.A. Gallegos, \( \mathcal{N} \) = 1 \( \mathcal{D} \) = 3 Lifshitz-Wess-Zumino model: a paradigm of reconciliation between Lifshitz-like operators and supersymmetry, Phys. Lett. B 793 (2019) 372 [arXiv:1806.01481] [INSPIRE].
R. Auzzi, S. Baiguera, G. Nardelli and S. Penati, Renormalization properties of a Galilean Wess-Zumino model, JHEP 06 (2019) 048 [arXiv:1904.08404] [INSPIRE].
D. Orlando and S. Reffert, On the perturbative expansion around a Lifshitz point, Phys. Lett. B 683 (2010) 62 [arXiv:0908.4429] [INSPIRE].
R. Dijkgraaf, D. Orlando and S. Reffert, Relating field theories via stochastic quantization, Nucl. Phys. B 824 (2010) 365 [arXiv:0903.0732] [INSPIRE].
S. Chapman, Y. Oz and A. Raviv-Moshe, On supersymmetric Lifshitz field theories, JHEP 10 (2015) 162 [arXiv:1508.03338] [INSPIRE].
G. Parisi and N. Sourlas, Supersymmetric field theories and stochastic differential equations, Nucl. Phys. B 206 (1982) 321 [INSPIRE].
E. Witten, Constraints on supersymmetry breaking, Nucl. Phys. B 202 (1982) 253 [INSPIRE].
E. Witten, Dynamical breaking of supersymmetry, Nucl. Phys. B 188 (1981) 513 [INSPIRE].
N. Sourlas, Introduction to supersymmetry in condensed matter physics, Physica D 15 (1985) 115.
E. Witten, Supersymmetry and Morse theory, J. Diff. Geom. 17 (1982) 661 [INSPIRE].
P.H. Damgaard and H. Huffel, Stochastic quantization, Phys. Rept. 152 (1987) 227 [INSPIRE].
D. Anselmi and M. Halat, Renormalization of Lorentz violating theories, Phys. Rev. D 76 (2007) 125011 [arXiv:0707.2480] [INSPIRE].
D. Anselmi, Weighted scale invariant quantum field theories, JHEP 02 (2008) 051 [arXiv:0801.1216] [INSPIRE].
O. Bergman, Nonrelativistic field theoretic scale anomaly, Phys. Rev. D 46 (1992) 5474 [INSPIRE].
S.P. Martin, A supersymmetry primer, Adv. Ser. Direct. High Energy Phys. 21 (2010) 1 [Adv. Ser. Direct. High Energy Phys. 18 (1998) 1] [hep-ph/9709356] [INSPIRE].
A.D. Dolgallo and K.N. Ilinski, Holomorphic supersymmetric quantum mechanics, generalized supersymmetry, and parasupersymmetry, Annals Phys. 236 (1994) 219.
A.M. Jaffe, A. Lesniewski and M. Lewenstein, Ground state structure in supersymmetric quantum mechanics, Annals Phys. 178 (1987) 313 [INSPIRE].
I. Arav, Y. Oz and A. Raviv-Moshe, Lifshitz anomalies, Ward identities and split dimensional regularization, JHEP 03 (2017) 088 [arXiv:1612.03500] [INSPIRE].
M. Visser, Lorentz symmetry breaking as a quantum field theory regulator, Phys. Rev. D 80 (2009) 025011 [arXiv:0902.0590] [INSPIRE].
T. Fujimori, T. Inami, K. Izumi and T. Kitamura, Tree-level unitarity and renormalizability in Lifshitz scalar theory, PTEP 2016 (2016) 013B08 [arXiv:1510.07237] [INSPIRE].
A.L. Fitzpatrick et al., A new theory of anyons, arXiv:1205.6816 [INSPIRE].
J. Alexandre, Lifshitz-type quantum field theories in particle physics, Int. J. Mod. Phys. A 26 (2011) 4523 [arXiv:1109.5629] [INSPIRE].
J. Alexandre and J. Brister, Fermion effective dispersion relation for z = 2 Lifshitz QED, Phys. Rev. D 88 (2013) 065020 [arXiv:1307.7613] [INSPIRE].
Y. Hahn and W. Zimmermann, An elementary proof of dyson’s power counting theorem, Commun. Math. Phys. 10 (1968) 330.
S. Weinberg, High-energy behavior in quantum field theory, Phys. Rev. 118 (1960) 838 [INSPIRE].
G. Leibbrandt and J. Williams, Split dimensional regularization for the Coulomb gauge, Nucl. Phys. B 475 (1996) 469 [hep-th/9601046] [INSPIRE].
G. Leibbrandt, The three point function in split dimensional regularization in the Coulomb gauge, Nucl. Phys. B 521 (1998) 383 [hep-th/9804109] [INSPIRE].
J. Wess and J. Bagger, Supersymmetry and supergravity, Princeton University Press, Princeton U.S.A. (1992).
H.K. Dreiner, H.E. Haber and S.P. Martin, Two-component spinor techniques and Feynman rules for quantum field theory and supersymmetry, Phys. Rept. 494 (2010) 1 [arXiv:0812.1594] [INSPIRE].
R. Shankar, Renormalization group approach to interacting fermions, Rev. Mod. Phys. 66 (1994) 129 [cond-mat/9307009] [INSPIRE].
J. Polchinski, Effective field theory and the Fermi surface, in the proceedings of the Theoretical Advanced Study Institute (TASI 92): From Black Holes and Strings to Particles, June 1–26, Boulder, U.S.A. (1992), hep-th/9210046 [INSPIRE].
A. Azzollini and A. Pomponio, Compactness results and applications to some “zero mass” elliptic problems, Nonlinear Anal. 69 (2008) 3559 [math/0601410].
H. Berestycki and P.L. Lions, Nonlinear scalar field equations. I. Existence of a ground state, Arch. Rational Mech. Anal. 82 (1983) 313.
H. Berestycki and P.L. Lions, Nonlinear scalar field equations. II. Existence of infinitely many solutions, Arch. Rational Mech. Anal. 82 (1983) 347.
O. Aharony and V. Narovlansky, Renormalization group flow in field theories with quenched disorder, Phys. Rev. D 98 (2018) 045012 [arXiv:1803.08534] [INSPIRE].
G. Gruner, The dynamics of charge-density waves, Rev. Mod. Phys. 60 (1988) 1129 [INSPIRE].
G. Gruner, The dynamics of spin-density waves, Rev. Mod. Phys. 66 (1994) 1 [INSPIRE].
M. Vojta, Lattice symmetry breaking in cuprate superconductors: stripes, nematics, and superconductivity, Adv. Phys. 58 (2009) 699.
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ArXiv ePrint: 1908.03220
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Arav, I., Oz, Y. & Raviv-Moshe, A. Holomorphic structure and quantum critical points in supersymmetric Lifshitz field theories. J. High Energ. Phys. 2019, 64 (2019). https://doi.org/10.1007/JHEP11(2019)064
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DOI: https://doi.org/10.1007/JHEP11(2019)064