Generalized uncertainty principle as a consequence of the effective field theory. (English) Zbl 1369.81084
Summary: We demonstrate that the generalized uncertainty principle exists because of the derivative expansion in the effective field theories. This is because in the framework of the effective field theories, the minimum measurable length scale has to be integrated away to obtain the low energy effective action. We analyze the deformation of a massive free scalar field theory by the generalized uncertainty principle, and demonstrate that the minimum measurable length scale corresponds to a second more massive scale in the theory, which has been integrated away. We also analyze CFT operators dual to this deformed scalar field theory, and observe that scaling of the new CFT operators indicates that they are dual to this more massive scale in the theory. We use holographic renormalization to explicitly calculate the renormalized boundary action with counter terms for this scalar field theory deformed by generalized uncertainty principle, and show that the generalized uncertainty principle contributes to the matter conformal anomaly.
MSC:
| 81T40 | Two-dimensional field theories, conformal field theories, etc. in quantum mechanics |
| 81R15 | Operator algebra methods applied to problems in quantum theory |
References:
| [1] | Amati, D.; Ciafaloni, M.; Veneziano, G., Phys. Lett. B, 216, 41 (1989) |
| [2] | Dzierzak, P.; Jezierski, J.; Malkiewicz, P.; Piechocki, W., Acta Phys. Pol. B, 41, 717 (2010) · Zbl 1371.83068 |
| [3] | Capozziello, S.; Lambiase, G.; Scarpetta, G., Int. J. Theor. Phys., 39, 15 (2000) · Zbl 0981.83021 |
| [4] | Caianiello, E. R., Lett. Nuovo Cimento, 32, 65 (1981) |
| [5] | Caianiello, E. R., Lett. Nuovo Cimento, 41, 370 (1984) |
| [6] | Capozziello, S.; Stornaiolo, C., Int. J. Geom. Methods Mod. Phys., 5, 185 (2008) · Zbl 1157.83317 |
| [7] | Maggiore, M., Phys. Lett. B, 304, 65 (1993) |
| [8] | Park, M. I., Phys. Lett. B, 659, 698 (2008) · Zbl 1246.83141 |
| [9] | Das, S.; Vagenas, E. C., Phys. Rev. Lett., 101, Article 221301 pp. (2008) |
| [10] | Liu, M.; Gui, Y.; Liu, H., Phys. Rev. D, 78, Article 124003 pp. (2008) |
| [11] | Chang, L. N.; Lewis, Z.; Minic, D.; Takeuchi, T., Adv. High Energy Phys., 2011, 493514 (2011) · Zbl 1234.81093 |
| [12] | Easther, R.; Greene, B. R.; Kinney, W. H.; Shiu, G., Phys. Rev. D, 67, Article 063508 pp. (2003) · Zbl 1222.83194 |
| [13] | Garay, L. J., Int. J. Mod. Phys. A, 10, 145 (1995) |
| [14] | Maggiore, M., Phys. Lett. B, 304, 65 (1993) |
| [15] | Ali, A. F.; Das, S.; Vagenas, E. C., Phys. Rev. D, 84, Article 044013 pp. (2011) |
| [16] | Husain, V.; Kothawala, D.; Seahra, S. S., Phys. Rev. D, 87, Article 025014 pp. (2013) |
| [17] | Faizal, M.; Kruglov, S. I., Int. J. Mod. Phys. D, 25, 1650013 (2016) · Zbl 1337.81083 |
| [18] | Faizal, M.; Khalil, M. M.; Das, S., Eur. Phys. J. C, 76, 30 (2016) |
| [19] | Kober, M., Phys. Rev. D, 82, Article 085017 pp. (2010) |
| [20] | Faizal, M., Int. J. Geom. Methods Mod. Phys., 12, 1550022 (2015) · Zbl 1309.81108 |
| [21] | Kober, M., Int. J. Mod. Phys. A, 26, 4251 (2011) · Zbl 1247.81631 |
| [22] | Maldacena, J. M., Adv. Theor. Math. Phys., 2, 231 (1998) · Zbl 0914.53047 |
| [23] | Gubser, S. S., Phys. Lett. B, 428, 105 (1998) |
| [24] | Aharony, O.; Gubser, S. S.; Maldacena, J. M.; Ooguri, H.; Oz, Y., Phys. Rep., 323, 183 (2000) · Zbl 1368.81009 |
| [25] | Skenderis, K., Class. Quantum Gravity, 19, 5849 (2002) · Zbl 1044.83009 |
| [26] | Aharony, O.; Jafferis, D.; Tomasiello, A.; Zaffaroni, A., J. High Energy Phys., 1011, Article 047 pp. (2010) |
| [27] | Witten, E., Adv. Theor. Math. Phys., 2, 253 (1998) · Zbl 0914.53048 |
| [28] | Mueck, W., Nucl. Phys. B, 620, 477 (2002) · Zbl 0988.81081 |
| [29] | de Haro, S.; Skenderis, K.; Solodukhin, S. N., Commun. Math. Phys., 217, 595 (2001) · Zbl 0984.83043 |
| [30] | Warner, N. P., Class. Quantum Gravity, 18, 3159 (2001) · Zbl 0995.83065 |
| [31] | Rehren, K. H., Ann. Henri Poincaré, 1, 607 (2000) · Zbl 1024.81026 |
| [32] | Rehren, K. H., Phys. Lett. B, 493, 383 (2000) · Zbl 1058.81610 |
| [33] | Kay, B. S.; Larkin, P., Phys. Rev. D, 77, Article 121501 pp. (2008) |
| [34] | Bertola, M.; Bros, J.; Moschella, U.; Schaeffer, R., Nucl. Phys. B, 587, 619 (2000) · Zbl 1043.81680 |
| [35] | ’t Hooft, G., Class. Quantum Gravity, 13, 1023 (1996) · Zbl 0855.53047 |
| [36] | Kostelecky, V. A.; Samuel, S., Phys. Rev. D, 39, 683 (1989) |
| [37] | Amelino-Camelia, G.; Ellis, J. R.; Mavromatos, N. E.; Nanopoulos, D. V.; Sarkar, S., Nature, 393, 763 (1998) |
| [38] | Gambini, R.; Pullin, J., Phys. Rev. D, 59, Article 124021 pp. (1999) |
| [39] | Carroll, S. M.; Harvey, J. A.; Kostelecky, V. A.; Lane, C. D.; Okamoto, T., Phys. Rev. Lett., 87, Article 141601 pp. (2001) |
| [40] | Horava, P., Phys. Rev. D, 79, Article 084008 pp. (2009) |
| [41] | Easther, R.; Greene, B. R.; Kinney, W. H.; Shiu, G., Phys. Rev. D, 64, Article 103502 pp. (2001) |
| [42] | Ali, M. Faizal. A.F.; Nassar, A., Int. J. Mod. Phys. A, 30, 1550183 (2015) · Zbl 1335.81119 |
| [43] | Ostrogradsky, M. V., Mem. Acad. St. Petersbourg VI, 4, 385 (1850) |
| [44] | Woodard, R. P., Lect. Notes Phys., 720, 403 (2007) |
| [45] | Hawking, S. W.; Hertog, T., Phys. Rev. D, 65, Article 103515 pp. (2002) |
| [46] | Fontanini, M.; Trodden, M., Phys. Rev. D, 83, Article 103518 pp. (2011) |
| [47] | Lee, T. D.; Wick, G. C., Nucl. Phys. B, 9, 209 (1969) · Zbl 0165.58203 |
| [48] | Lee, T. D.; Wick, G. C., Phys. Rev. D, 2, 1033 (1970) · Zbl 1227.81252 |
| [49] | Lee, T. D.; Wick, G. C., Phys. Rev. D, 3, 1046 (1971) |
| [50] | Grinstein, B.; O’Connell, D.; Wise, M. B., Phys. Rev. D, 77, Article 025012 pp. (2008) |
| [51] | Cho, I.; Kwon, O. K., Phys. Rev. D, 82, Article 025013 pp. (2010) |
| [52] | Dias, M.; Ferrari, A. F.; Palechor, C. A.; Senise, C. R., J. Phys. A, 48, 275403 (2015) · Zbl 1319.81076 |
| [53] | Faizal, M., Phys. Lett. B, 757, 244 (2016) · Zbl 1360.81210 |
| [54] | Becchi, C.; Rouet, A.; Stora, R., Ann. Phys., 98, 287 (1976) |
| [56] | Rivelles, V. O., Phys. Lett. B, 577, 137 (2003) · Zbl 1073.81633 |
| [57] | Andrzejewski, K.; Gonera, J.; Machalski, P.; Bolonek-Lason, K., Phys. Lett. B, 706, 427 (2012) |
| [58] | Faizal, M.; Khan, M., Eur. Phys. J. C, 71, 1603 (2011) |
| [59] | Mintchev, M., J. Phys. A, 13, 184 (1980) |
| [60] | Fradkin, E. S.; Tseytlin, A. A., Nucl. Phys. B, 201, 469 (1982) |
| [61] | Broadbridge, P., J. Phys. A, 16, 3271 (1983) · Zbl 0527.46057 |
| [62] | Barth, N. H.; Christensen, S. M., Phys. Rev. D, 28, 1876 (1983) |
| [63] | Moschella, U., J. Math. Phys., 31, 2480 (1990) · Zbl 0734.46048 |
| [64] | Asorey, M.; Lopez, J. L.; Shapiro, I. L., Int. J. Mod. Phys. A, 12, 5711 (1997) · Zbl 0902.53066 |
| [65] | Lukierski, J., Acta Phys. Pol., 32, 771 (1967) |
| [66] | de Urries, F. J.; Julve, J.; Sanchez, E. J., J. Phys. A, 34, 8919 (2001) · Zbl 0996.81047 |
| [67] | Cheng, T. C.; Ho, P. M.; Yeh, M. C., Nucl. Phys. B, 625, 151 (2002) · Zbl 0985.81125 |
| [68] | Nakanishi, N., Prog. Theor. Phys. Suppl., 51, 1 (1972) |
| [69] | Accioly, A.; Azeredo, A.; Mukai, H., J. Math. Phys., 43, 473 (2002) · Zbl 1052.83030 |
| [70] | Villasenor, E. J., J. Phys. A, 35, 6169 (2002) · Zbl 1066.81622 |
| [71] | Burgess, C. P., Annu. Rev. Nucl. Part. Sci., 57, 329 (2007) |
| [72] | Awad, A.; Faizal, M., J. High Energy Phys., 1510, Article 002 pp. (2015) |
| [73] | Morris, T. R., Phys. Lett. B, 329, 241 (1994) · Zbl 1190.81094 |
| [74] | Kim, C., Phys. Rev. D, 74, Article 067702 pp. (2006) |
| [75] | Bohr, N. E.J. B. (2004) |
| [76] | Hung, L. Y., J. High Energy Phys., 0804, Article 057 pp. (2008) |
| [77] | Banks, T. (2010) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
