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## Heat kernel expansion and induced action for matrix models (2011)

Citations: | 4 - 3 self |

### Citations

5608 | The large N limit of superconformal field theories and supergravity
- Maldacena
- 1998
(Show Context)
Citation Context ...2) reduces to the DBI action on a geometry with effective metric ds2 = H−1/2(x)dxµdxµ +H1/2(x)(dφ2 + φ2dΩ5) , H = 1 + Q |φ2|2 ≈ Q |φ2|2 for Q |φ2|2 1 . (44) This is consistent with IIB supergravity =-=[28, 29]-=-, and as is well-known, reduces to AdS5×S5 in the near-horizon limit. The result above is in fact more general, since the effective 4-dimensional brane metric Gµν is not necessarily flat. Therefore th... |

946 | An Introduction to Quantum Field Theory - Peskin, Schroeder - 1995 |

216 | The Fuzzy sphere - Madore - 1992 |

209 |
Born-Infeld action, supersymmetry and string theory, in The many faces of the superworld. Yuri Golfand memorial volume
- Tseytlin
(Show Context)
Citation Context ...(√∣∣∣∣ det(Gµν + Q|φ2|2DµφiDνφi + Q1/2|φ2| FµνΛ2NC )∣∣∣∣−√|detG| ) , Q = (N − 1) 2pi2Λ4NC , T3 = Λ 4 NC . (42) In string theory, these constants are known to be Q = (N−1)gsα ′2 pi and T3 = 1 2pigsα′2 =-=[27]-=-, which is consistent with the above result. In fact, it allows to identify the scale of non-commutativity with the string theory parameters as gsα ′2 = 1 2piΛ4NC . (43) The geometrical meaning of (42... |

113 |
A large-N reduced model as superstring, Nucl. Phys. B498
- Ishibashi, Kawai, et al.
- 1997
(Show Context)
Citation Context ...g scalars, fermions, gauge bosons and (emergent) gravity was originally introduced as a non-perturbative description of type IIB string theory: It is the so-called IKKT model, named after its authors =-=[4]-=-, and given by the action SIKKT = −(2pi)2Tr ( [Xa, Xb][Xa, Xb] + 2Ψγa[X a,Ψ] ) , (1) where Xa, a = 0, 1, 2, . . . , 9 are Hermitian matrices, Ψ is a matrix-valued Majorana-Weyl spinor of SO(9, 1), and... |

113 | Large N limit of non-commutative gauge theories,” JHEP 9909 - Maldacena, Russo - 1999 |

88 | Supergravity and large N noncommutative field theories,” JHEP 9911 - Alishahiha, Oz, et al. - 1999 |

82 | Non-commutative world-volume geometries - Alekseev, Schomerus - 1999 |

75 | Dielectric branes, JHEP 9912 - Myers - 1999 |

60 | Emergent Gravity from Noncommutative Gauge Theory
- Steinacker
(Show Context)
Citation Context .... . , D. Here we consider this submanifold to be a four dimensional space-time M4. However, it is not the induced metric which is “seen” by scalar fields, gauge fields, etc., but the effective metric =-=[11]-=- Gµν = e−σθµρθνσgρσ , e−σ ≡ √ det θ−1µν√ detGρσ . (6) 2 gµν(x) M2n Figure 1: Embedding and induced metric; projectors on the tangential/normal bundle ofM4 ∈ RD may be defined as PabT = gµν∂µxa∂νxb and... |

59 | Quantized gauge theory on the fuzzy sphere as random matrix model,” hep-th/0307075 - Steinacker - 2003 |

49 | Emergent Geometry and Gravity from Matrix Models: an Introduction,” arXiv:1003.4134 [hep-th
- Steinacker
(Show Context)
Citation Context ...are some recent results [1, 2] which are based on the idea of gravity as an emergent force derived from matrix models — for a general introduction to the subject, the interested reader is referred to =-=[3]-=-. It is indeed not easy to find a new model that is renormalizable, but a concept that is known to greatly improve the properties of a model with respect to divergences and renormalizability is supers... |

37 | Dynamical generation of fuzzy extra dimensions, dimensional reduction and symmetry breaking - Aschieri, Grammatikopoulos, et al. |

33 | Wilsonian effective actions and the IR/UV mixing in noncommutative gauge theories,” JHEP 0101 - Khoze, Travaglini - 2001 |

32 | Emergent Gravity and Noncommutative Branes from Yang-Mills Matrix Models
- Steinacker
(Show Context)
Citation Context ...ermitian matrices on H which in the semi-classical limit are interpreted as coordinate functions. If (in the simplest case) one considers some of the coordinates to be functions of the remaining ones =-=[10]-=- such that Xa ∼ xa = (xµ, φi(xµ)) in the semi-classical limit, one can interpret the xa as defining the embedding of a 2n-dimensional submanifold M2n ↪→ RD equipped with a non-trivial induced metric (... |

31 | Effective actions of matrix models on homogeneous spaces - Imai, Kitazawa, et al. |

22 |
Intersecting branes and a standard model realization in matrix models [arXiv:1107.0265
- Chatzistavrakidis, Steinacker, et al.
(Show Context)
Citation Context ...sional space-time within the IKKT model has been obtained recently in Ref. [6], providing further motivation to study the effective physics of 4-dimensional backgrounds. Additionally, it was shown in =-=[7]-=- how the particle spectrum of the standard model may be correctly reproduced from that action by considering specific brane solutions, hence showing how realistic physics may emerge from the IKKT mode... |

17 | Heat kernel and number theory on NC-torus
- Gayral, Iochum, et al.
(Show Context)
Citation Context ...be generated without SUSY cancellations, and we will of course need a UV cutoff there. In fact, it is what we demand of this cutoff, that differs the present expansion from previous work: It is known =-=[18, 19]-=-, that taking Λ→∞ while keeping ΛNC fixed leads to pathological behaviour of the heat kernel expansion such as problematic UV/IR mixing. Hence, we demand [1] that the quantity (p) := p2Λ2/Λ4NC 1 , ... |

16 |
Split noncommutativity and compactified brane solutions in matrix models
- Steinacker
(Show Context)
Citation Context ...notes some compact manifold. A gravitational action is then induced on the brane below the SUSY breaking scale, as suggested in [10]. Some simple examples of possible geometries are discussed in Ref. =-=[16]-=- — see also [17] for related discussions. In Section 4 we will consider only the fermionic action in order to get an idea of what types of terms will be generated without SUSY cancellations, and we wi... |

16 |
Heat kernel, effective action and anomalies
- Vassilevich
- 2005
(Show Context)
Citation Context ...be generated without SUSY cancellations, and we will of course need a UV cutoff there. In fact, it is what we demand of this cutoff, that differs the present expansion from previous work: It is known =-=[18, 19]-=-, that taking Λ→∞ while keeping ΛNC fixed leads to pathological behaviour of the heat kernel expansion such as problematic UV/IR mixing. Hence, we demand [1] that the quantity (p) := p2Λ2/Λ4NC 1 , ... |

15 |
Expanding (3+1)-dimensional universe from a Lorentzian matrix model for superstring theory
- Kim, Nishimura, et al.
(Show Context)
Citation Context ...well-defined quantum theory at least for 4-dimensional backgrounds. In fact, numerical evidence for the emergence of 3+1dimensional space-time within the IKKT model has been obtained recently in Ref. =-=[6]-=-, providing further motivation to study the effective physics of 4-dimensional backgrounds. Additionally, it was shown in [7] how the particle spectrum of the standard model may be correctly reproduce... |

14 |
Curvature and Gravity Actions for Matrix Models II: the case of general Poisson structure
- Blaschke, Steinacker
(Show Context)
Citation Context ...ill be on the one-loop effective action of the IKKT model. 2 The idea of emergent gravity from matrix models Before we proceed, we ought to explain how gravity may emerge from such matrix models (cf. =-=[3, 8, 9]-=-). This is best shown by considering the bosonic part of the action (1), namely SYM = −Tr[Xa, Xb][Xc, Xd]ηacηbd . (4) The Xa are Hermitian matrices on H which in the semi-classical limit are interpret... |

13 | Perturbative versus nonperturbative dynamics of the fuzzy - Azuma, Bal, et al. |

12 | Effective Gauge Theories - Weinberg - 1980 |

10 |
On the 1-loop effective action for the IKKT model and non-commutative branes
- Blaschke, Steinacker
- 2011
(Show Context)
Citation Context ...gy limit ki → 0, while NC effects are sub-leading. This means, that in the supersymmetric case one may expect the low-energy effective action to reduce to N = 4 SYM on a general background M. In Ref. =-=[2]-=-, it was shown that the effective action for an unbroken massless gauge boson in the Coulomb phase on a generic curved brane leads to the leading terms of the Dirac-BornInfeld (DBI) action for a singl... |

10 |
Ultra-violet finiteness in noncommutative supersymmetric theories
- Jack, Jones
(Show Context)
Citation Context ...try, (3) where the tilde indicates the corresponding spin group. Although an explicit proof to all orders is still missing, there are good reasons to believe that this model is in fact renormalizable =-=[4, 5]-=-. Here we take the IKKT matrix model model (1) as a starting point independent of string theory, and focus on 4-dimensional brane solutions or backgrounds, considered as physical space(-time). Due to ... |

6 | Quantum effective potential for U(1) fields - Castro-Villarreal, Delgadillo-Blando, et al. - 2005 |

6 | Fermions and noncommutative emergent gravity II: Curved branes in extra dimensions,” arXiv:0909.5298 [hep-th
- Klammer, Steinacker
(Show Context)
Citation Context ...ily possible to further generalize the model to include curvature terms of type∫ d4x (2pi)2 √ gΛ(x)2 ( R+ (Λ̄4NCe −σθµρθηαRµρηα − 4R) + c′∂µσ∂µσ ) , (39) which should also appear, as was discussed in =-=[1, 9, 25, 26]-=-. These would then be higher-order commutator terms, as indicated by “h.o.” in Eqn. (38). 5 Non-Abelian sector Non-Abelian gauge fields appear when one considers a background of N coinciding branes, i... |

6 |
Two loop N = 4 super Yang-Mills effective action and interaction between D3-branes, Nucl.Phys. B621
- Buchbinder, Petrov, et al.
- 2002
(Show Context)
Citation Context ...2) reduces to the DBI action on a geometry with effective metric ds2 = H−1/2(x)dxµdxµ +H1/2(x)(dφ2 + φ2dΩ5) , H = 1 + Q |φ2|2 ≈ Q |φ2|2 for Q |φ2|2 1 . (44) This is consistent with IIB supergravity =-=[28, 29]-=-, and as is well-known, reduces to AdS5×S5 in the near-horizon limit. The result above is in fact more general, since the effective 4-dimensional brane metric Gµν is not necessarily flat. Therefore th... |

4 |
On Lie-algebraic solutions of the type IIB matrix model [arXiv:1108.1107
- Chatzistavrakidis
(Show Context)
Citation Context ...ct manifold. A gravitational action is then induced on the brane below the SUSY breaking scale, as suggested in [10]. Some simple examples of possible geometries are discussed in Ref. [16] — see also =-=[17]-=- for related discussions. In Section 4 we will consider only the fermionic action in order to get an idea of what types of terms will be generated without SUSY cancellations, and we will of course nee... |

2 | Trek: The One loop N = 4 noncommutative SYM action, Nucl.Phys. B614 - Liu, Michelson - 2001 |