Review
Anomaly Non-Renormalization, Lattice QFT, and Universality of Transport Coefficients
Vieri Mastropietro,
Corresponding Author
Vieri Mastropietro
Department of Mathematics, University of Milan, via C. Saldini 50, Milan, 20129 Italy
E-mail: [email protected]
Search for more papers by this authorVieri Mastropietro,
Corresponding Author
Vieri Mastropietro
Department of Mathematics, University of Milan, via C. Saldini 50, Milan, 20129 Italy
E-mail: [email protected]
Search for more papers by this authorFirst published: 09 February 2024
Abstract
Recently new methods have been introduced to investigate the non-renormalization properties of the anomalies at a non perturbative level and in presence of a lattice. The issue is relevant in a number of problems ranging from the anomaly-free construction of chiral lattice gauge theory with large cut-off to the universality properties observed in transport coefficients in condensed matter systems. A review of main results and future perspectives is presented.
Conflict of Interest
The authors declare no conflict of interest.
References
- 1S. L. Adler, Phys. Rev. 1966, 177, 2426.
10.1103/PhysRev.177.2426 Google Scholar
- 2S. L. Adler, W. A. Bardeen, Phys. Rev. 1969, 182, 1517.
- 3H. Georgi J. M. Rawls, Phys. Rev. D 1971, 3, 874.
- 4A. Zee, Phys. Rev. Lett. 1972, 29, 1198.
- 5G. Costa, J. Julve, T. Marinucci, M. Tonin, Nuovo Cimento A 1977, 38, 373.
10.1007/BF02730012 Google Scholar
- 6G. Bandelloni, C. Becchi, A. Blasi, R. Collina, Commun. Mat. Phys. 1980, 72, 239.
- 7K. Fujikawa, Phys. Rev. Lett. 1979, 42, 1195.
- 8S. L. Adler, Anomalies at all orders. 50 Years of Yang-Mills Theory, World Scientific, Singapore 2005, pp. 187–228.
- 9C. Kopper, B. Lévêque, J. Math. Phys. 2012, 53, 022305.
10.1063/1.3686000 Google Scholar
- 10E. Seiler, I. O. Stamatescu, Phys. Rev. D 1982, 25, 2177.
- 11N. K. Nielsen, B. Schroer, Nucl. Phys. B 1977, 127, 493.
- 12S. Weinberg, Phys. Rev. Lett. 1967, 19, 1264.
- 13G. t Hooft, Nucl. Phys. 1971, 35, 167.
- 14C. Bouchiat, J. Iliopoulos, P. Meyer, Phys. Lett. B 1972, 38, 519.
10.1016/0370-2693(72)90532-1 Google Scholar
- 15K. Fredenhagen, K. Rehren, E. Seiler, Lect. Notes Phys. 2007, 721, 61.
- 16R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, A. K. Geim, Science 2008, 320, 1308.
- 17J. Fröhlich, B. Pedrini, in Mathematical Physics 2000, (Eds.: A. Fokas, A. Grigoryan, T. Kibble, B. Zegarlinski), Imperial College Press, London and Singapore 2000, p. 947.
- 18G. W. Semenoff, Phys. Rev. Lett. 1984, 53, 2449.
- 19D. M. Haldane, Phys. Rev. Lett. 1988, 61, 2015.
- 20H. B. Nielsen, M. Ninomiya, Phys. Lett. B 1983, 130, 389.
- 21S. I. Tomonaga, Prog. Theor. Phys. 1950, 5, 544.
- 22S. Coleman, B. Hill, Phys. Lett. B 1985, 159, 184.
- 23K. Ishikawa, T. Matsuyama, Z. Phys C. 1986, 33, 4145.
10.1007/BF01410451 Google Scholar
- 24J. Fröhlich, Nucl. Phys. B 1982, 200, 281.
- 25M. Aizenman, H. Duminil-Copin, Ann. Math. 2021, 194, 163.
- 26J.-S. Feldman, T. R. Hurd, L. Rosen, J. D. Wright, Lect. Notes Phys. 1988, 312, 1.
10.1007/3-540-50213-0_9 Google Scholar
- 27T. Hurd, Com. mun. Math. Phys. 1989, 125, 515 L. Rosen, J. D. Wright, Commun. Math. Phys. 1990, 134, 433.
- 28T. Hurd, Commun. Math. Phys. 1989, 120, 469.
- 29G. Gallavotti, Rev. Mod. Phys. 1985, 57, 471.
- 30G. Keller, C. Kopper, Commun. Math. Phys. 1996, 176, 193.
- 31G. Keller, C. Kopper, M. Salmhofer, Helv. Phys. Acta 1991, 65, 3252.
- 32A. N. Efremov, R. Guida, C. Kopper, J. Math. Phys. 2017, 58, 093503.
10.1063/1.5000041 Google Scholar
- 33J. Polchinski, Theoretical advanced study in theoretical physics: Recent directions in particle physics theory, Boulder, 1–26, 235–274 (1992).
- 34J. Dimock, T. D. Hurd, J. Math. Phys. 1992, 33, 814.
- 35A. Borrelli, L. Maiani, G. C. Rossi, R. Sisto, M. Testa, Phys. Lett. B 1989, 221, 360 Nucl. Phys. B 1990, 333, 335.
- 36D. B. Kaplan, Phys. Lett. B 1992, 288, 342.
- 37R. Narayanan, H. Neuberger, Phys. Lett. B 1993, 302, 62.
- 38M. Testa, PCTP - ICTP Joint International Conference (AIJIC 97) on Recent Developments in Nonperturbative Quantum Field Theory, World Scientific, Singapore, pp. 114–127.
- 39M. Luscher, Nucl. Phys. B 1999, 549, 295.
- 40M. Luscher, JHEP 2000, 0006, 028.
10.1088/1126-6708/2000/06/028 Google Scholar
- 41H. Neuberger, Phys. Rev. D 2001, 63, 014503.
10.1103/PhysRevD.63.014503 Google Scholar
- 42D. M. Grabowska, D. B. Kaplan, Phys. Rev. Lett. 2016, 116, 211602.
- 43J. Wang, X.-G. Wen, Phys. Rev. Res. 2020, 2, 023356.
- 44M. Golterman, Nucl. Phys. B (Proc. Suppl.) 2001, 94, 189.
- 45E. Poppitz, Int. J. Modern Phys. A 2010, 25, 2761.
- 46A. K. De, Indian J. Phys. 2021, 95, 1639.
- 47M. I. Katsnelson, Graphene, Cambridge University Press 2012.
- 48E. G. Mishchenko, Phys. Rev. Lett. 2007, 98, 216801.
- 49I. F. Herbut, V. Juricic, O. Vafek, Phys. Rev. Lett. 2008, 100, 046403.
- 50D. E. Sheehy, J. Schmalian, Phys. Rev. B 2009, 80, 193411.
- 51D. L. Boyda, V. V. Braguta, M. I. Katsnelson, M. V. Ulybyshev, Phys. Rev. B 2016, 94, 085421.
- 52A. A. Burkov, L. Balents, Phys. Rev. Lett. 2011, 107, 127205.
- 53D. T. Son, B. Z. Spivak, Phys. Rev. B 2013, 88, 104412.
- 54J. Xiong, S. K. Kushwaha, T. Liang, J. W. Krizan, M. Hirschberger, W. Wang, R. J. Cava, N. P. Ong, Science 2015, 350, 413.
- 55A. Avdoshkin, V. Kozii, J. E. Moore, Phys. Rev. Lett. 2020, 124, 196603.
- 56H. B. Nielsen, M. Ninomiya, Phys. Lett. B. 1981, 105, 219.
- 57T. Stauber, N. M. R. Peres, A. K. Geim, Phys. Rev. B 2008, 78, 085432.
- 58A. Giuliani, V. Mastropietro, M. Porta, Comm. Math. Phys. 2021, 384, 9971060.
- 59V. Mastropietro, J. Math. Phys. 2023, 64, 032303.
10.1063/5.0093162 Google Scholar
- 60V. Mastropietro, J. Math. Phys. 2007, 48, 102303.
10.1063/1.2800156 Google Scholar
- 61A. Giuliani, V. Mastropietro, Comm. Math. Phys. 2010, 293, 301
Phys. Rev. B 2009, 79, 201403(R)
10.1103/PhysRevB.79.201403 Google ScholarErratum, ibid 2010, 82, 199901(E).
- 62D. Brydges, A short course on Cluster Expansions, Les Houches 1984, (Eds.: K. Osterwalder, R. Stora), North Holland Press, 1986.
- 63V. Mastropietro, Non-perturbative renormalization, World Scientific, Singapore 2008.
10.1142/6748 Google Scholar
- 64V. Mastropietro, JHEP 2020, 95.
- 65V. Mastropietro, J. Phys. A: Math. Theor. 2014, 47, 465003
10.1088/1751-8113/47/46/465003 Google ScholarJ. Stat. Phys. 2014, 157, 830.
- 66A. Giuliani, V. Mastropietro, M. Porta, Phys. Rev. B 2011, 83, 195401;
10.1103/PhysRevB.83.195401 Google ScholarComm. Math. Phys. 2012, 311, 317.
- 67A. Giuliani, V. Mastropietro, M. Porta, Comm. Math. Phys. 2017, 349, 1107.
- 68A. Giuliani, I. Jauslin, V. Mastropietro, M. Porta, Phys. Rev. B 2016, 94, 205139.
10.1103/PhysRevB.94.205139 Google Scholar
- 69D. C. Elias, R. V. Gorbachev, A. S. Mayorov, S. V. Morozov, A. A. Zhukov, P. Blake, L. A. Ponomarenko, I. V. Grigorieva, K. S. Novoselov, F. Guinea A. K. Geim, Nat. Phys. 2011, 7, 701704.
10.1038/nphys2049 Google Scholar
- 70W. W. Ludwig, Matthew P. A. Fisher, R. Shankar, G. Grinstein, Phys. Rev. B 1994, 50, 7526.
- 71A. Giuliani, V. Mastropietro, M. Porta, Annals Phys. 2012, 327, 461.
- 72G. Benfatto V. Mastropietro, Commun. Math. Phys. 2005, 258, 609.
- 73V. Mastropietro, J. Math. Phys. 2007, 48, 022302.
10.1063/1.2436731 Google Scholar
- 74G. Benfatto, P. Falco, V. Mastropietro, Commun. Math. Phys. 2007, 273, 67.
- 75V. Rivasseau, From Perturbative to Constructive Renormalization, Princeton University Press 1991.
- 76J. Gonzalez, F. Guinea, M. A. H. Vozmediano, Nucl. Phys. B 1994, 424, 595.
- 77A. Giuliani V. Mastropietro, Phys. Rev. B 2012, 85, 045420.
10.1103/PhysRevB.85.045420 Google Scholar
- 78I. Herbut, V. Mastropietro, Phys. Rev. B 2013, 87, 205445.
10.1103/PhysRevB.87.205445 Google Scholar
- 79V. Mastropietro, Phys. Rev. D 2021, 103, 013009.
- 80V. Mastropietro, Vanishing of the Anomaly in Lattice Chiral Gauge Theory Vieri Mastropietro Annales Henri Poincaré 2023.
- 81V. Mastropietro, Phys. Rev. D 2022, 105, 114502.
- 82C. M. Sommerfield, Ann. Phys. 1964, 26, 143.
10.1016/0003-4916(64)90273-8 Google Scholar
- 83a) G. Benfatto, P. Falco, V. Mastropietro, Comm. Math. Phys. 2007, 273, 67; b) G. Benfatto, P. Falco, V. Mastropietro, Phys. Rev. Lett. 2010, 104, 075701.
- 84G. Benfatto, V. Mastropietro, J. Stat. Phys. 2011, 138, 1084.
- 85G. Benfatto, V. Mastropietro, J. Stat. Phys. 2011, 143, 251.
- 86V. Mastropietro, Phys. Rev. E 2013, 87, 042121.
10.1103/PhysRevE.87.042121 Google Scholar
- 87G. Benfatto, P. Falco, V. Mastropietro, Comm. Math. Phys. 2014, 330, 153.
- 88V. Mastropietro, M. Porta, Comm. Math. Phys. 2022, 395, 1097.
