Heat kernel expansion and induced action for the matrix model Dirac operator

Journal of High Energy Physics

Volumn 2011, Issue 3, 2011, Pages

  Blaschke, Daniel N ^a   Steinacker, Harold ^a   Wohlgenannt, Michael ^a,b  

^a UNIVERSITY OF VIENNA   (Austria)

^b VIENNA UNIVERSITY OF TECHNOLOGY   (Austria)

Author keywords

Gauge symmetry; Gauge gravity correspondence; M(atrix) theories; Non commutative geometry

Indexed keywords

EID: 80053097210     PISSN: 11266708     EISSN: 10298479     Source Type: Journal    
DOI: 10.1007/JHEP03(2011)002     Document Type: Article

References (31)

1. H. Aoki et al., Noncommutative Yang-Mills in IIB matrix model, Nucl. Phys. B 565 (2000) 176 [hep-th/9908141] [SPIRES].
2. H. Steinacker, Emergent Gravity from Noncommutative Gauge Theory, JHEP 12 (2007) 049 [arXiv:0708.2426] [SPIRES].
3. H. Steinacker, Emergent Gravity and Noncommutative Branes from Yang-Mills Matrix Models, Nucl. Phys. B 810 (2009) 1 [arXiv:0806.2032] [SPIRES].
4. H. Steinacker, Emergent Geometry and Gravity from Matrix Models: an Introduction, Class. Quant. Grav. 27 (2010) 133001 [arXiv:1003.4134] [SPIRES].
5. A.D. Sakharov, Vacuum quantum fluctuations in curved space and the theory of gravitation, Sov. Phys. Dokl. 12
6. N. Ishibashi, H. Kawai, Y. Kitazawa and A. Tsuchiya, A Large-N Reduced Model As Superstring, Nucl. Phys. B 498 (1997) 467 [hep-th/9612115] [SPIRES].
7. T. Imai, Y. Kitazawa, Y. Takayama and D. Tomino, Effective actions of matrix models on homogeneous spaces, Nucl. Phys. B 679 (2004) 143 [hep-th/0307007] [SPIRES].
8. 2 , JHEP 09 (2005) 066 [hep-th/0506044] [SPIRES].
9. H. Steinacker, Quantized gauge theory on the fuzzy sphere as random matrix model, Nucl. Phys. B 679 (2004) 66 [hep-th/0307075] [SPIRES].
10. 2, JHEP 09 (2005) 047 [hep-th/0506205] [SPIRES].
11. H. Grosse, H. Steinacker and M. Wohlgenannt, Emergent Gravity, Matrix Models and UV/IR Mixing, JHEP 04 (2008) 023 [arXiv:0802.0973] [SPIRES].
12. V. Gayral, B. Iochum and D.V. Vassilevich, Heat kernel and number theory on NC-torus, Commun. Math. Phys. 273 (2007) 415 [hep-th/0607078] [SPIRES].
13. D.V. Vassilevich, Heat kernel, effective action and anomalies in noncommutative theories, JHEP 08 (2005) 085 [hep-th/0507123] [SPIRES].
14. A. Armoni, Comments on perturbative dynamics of non-commutative Yang-Mills theory, Nucl. Phys. B 593 (2001) 229 [hep-th/0005208] [SPIRES].
15. J.M. Drummond, J.M. Henn and J. Plefka, Yangian symmetry of scattering amplitudes in N = 4 super Yang-Mills theory, JHEP 05 (2009) 046 [arXiv:0902.2987] [SPIRES].
16. N. Beisert, J. Henn, T. McLoughlin and J. Plefka, One-Loop Superconformal and Yangian Symmetries of Scattering Amplitudes in N = 4 Super Yang-Mills, JHEP 04 (2010) 085 [arXiv:1002.1733] [SPIRES].
17. Z. Bern, L.J. Dixon and D.A. Kosower, All next-to-maximally helicity-violating one-loop gluon amplitudes in N = 4 super-Yang-Mills theory, Phys. Rev. D 72 (2005) 045014 [hep-th/0412210] [SPIRES].
18. N. Arkani-Hamed, J.L. Bourjaily, F. Cachazo, S. Caron-Huot and J. Trnka, The All-Loop Integrand For Scattering Amplitudes in Planar N = 4 SYM, JHEP 01 (2011) 041 [arXiv:1008.2958] [SPIRES].
19. A.H. Chamseddine and A. Connes, The spectral action principle, Commun. Math. Phys. 186 (1997) 731 [hep-th/9606001] [SPIRES].
20. D. Klammer and H. Steinacker, Fermions and Emergent Noncommutative Gravity, JHEP 08 (2008) 074 [arXiv:0805.1157] [SPIRES].
21. D. Klammer and H. Steinacker, Fermions and noncommutative emergent gravity II: Curved branes in extra dimensions, JHEP 02 (2010) 074 [arXiv:0909.5298] [SPIRES].
22. P.B. Gilkey, Invariance theory, the heat equation and the Atiyah-Singer index theorem, second edition, CRC Press Inc., Boca Raton U.S.A. (1995).
23. D.V. Vassilevich, Heat kernel expansion: User's manual, Phys. Rept. 388 (2003) 279 [hep-th/0306138] [SPIRES].
24. R.J. Szabo, Quantum Field Theory on Noncommutative Spaces, Phys. Rept. 378 (2003) 207 [hep-th/0109162] [SPIRES].
25. D.N. Blaschke, E. Kronberger, R.I.P. Sedmik and M. Wohlgenannt, Gauge Theories on Deformed Spaces, SIGMA 6 (2010) 062 [arXiv:1004.2127] [SPIRES].
26. I. Jack and D.R.T. Jones, Ultra-violet finiteness in noncommutative supersymmetric theories, New J. Phys. 3 (2001) 19 [hep-th/0109195] [SPIRES].
27. N. Sasakura, Heat kernel coefficients for compact fuzzy spaces, JHEP 12 (2004) 009 [hep-th/0411029] [SPIRES].
28. D.N. Blaschke and H. Steinacker, Curvature and Gravity Actions for Matrix Models, Class. Quant. Grav. 27 (2010) 165010 [arXiv:1003.4132] [SPIRES].
29. D.N. Blaschke and H. Steinacker, Curvature and Gravity Actions for Matrix Models II: the case of general Poisson structure, Class. Quant. Grav. 27 (2010) 235019 [arXiv:1007.2729] [SPIRES].
30. H. Steinacker, Covariant Field Equations, Gauge Fields and Conservation Laws from Yang-Mills Matrix Models, JHEP 02 (2009) 044 [arXiv:0812.3761] [SPIRES].
31. H. Grosse and M. Wohlgenannt, Induced gauge theory on a noncommutative space, Eur. Phys. J. C 52 (2007) 435 [hep-th/0703169] [SPIRES].