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

Blaschke, Daniel N.; Steinacker, Harold; Wohlgenannt, Michael

doi:10.1007/jhep03(2011)002

Cited by 15 publications

(38 citation statements)

References 44 publications

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“…This explanation of UV/IR mixing holds in the semi-classical regime i.e. for low enough cutoff, and has been verified in detail [21,33] that these induced gravity terms give e.g. (10.4) in the appropriate limit.…”

Section: Uv/ir Mixing In Noncommutative Gauge Theorymentioning

confidence: 61%

“…Similarly, the information about the geometry of M is encoded in the spectrum of its Laplacian or Dirac operator below its cutoff. It turns out that such a cutoff is in fact essential to obtain meaningful Seeley-de Witt coefficients in the noncommutative case [21]. We can thus formulate a specific way to associate an effective geometry to a noncommutative space with Laplacian : if spec has a clear enough asymptotics for Λ ≤ Λ max and approximately coincides with spec∆ g for some classical manifold (M , g) for Λ ≤ Λ max , then its spectral geometry is that of (M , g).…”

Section: Spectral Matrix Geometrymentioning

confidence: 99%

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Non-commutative geometry and matrix models

Steinacker¹

2013

Proceedings of 3rd Quantum Gravity and Quantum Geometry School — PoS(QGQGS 2011)

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These notes provide an introduction to the noncommutative matrix geometry which arises within matrix models of Yang-Mills type. Starting from basic examples of compact fuzzy spaces, a general notion of embedded noncommutative spaces (branes) is formulated, and their effective Riemannian geometry is elaborated. This class of configurations is preserved under small deformations, and is therefore appropriate for matrix models. A realization of generic 4-dimensional geometries is sketched, and the relation with spectral geometry and with noncommutative gauge theory is explained. In a second part, dynamical aspects of these matrix geometries are considered. The one-loop effective action for the maximally supersymmetric IKKT or IIB matrix model is discussed, which is well-behaved on 4-dimensional branes.

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Section: Uv/ir Mixing In Noncommutative Gauge Theorymentioning

confidence: 61%

Section: Spectral Matrix Geometrymentioning

confidence: 99%

Non-commutative geometry and matrix models

Steinacker¹

2013

Proceedings of 3rd Quantum Gravity and Quantum Geometry School — PoS(QGQGS 2011)

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“…Given a representation H n of SO(4, 2), the most general "function" in End(H n ) can always be expanded as follows 42) which transform in the adjoint representation M ab → [M ab , ·] of so(4, 2). The φ ab (X) will be interpreted as quantized tensor fields on H 4 , which transform under SO(4, 1).…”

Section: Wave-functions and Spin Casimirmentioning

confidence: 99%

“…22. On Moyal-Weyl backgrounds, N = 1 SUSY is sufficient to cancel the induced "would-be" cosmological constant term, while the induced Einstein-Hilbert term is only canceled in the N = 4 case[41,42]. This is reflected by the absence of UV/IR mixing.…”

mentioning

confidence: 99%

The fuzzy 4-hyperboloid Hn4 and higher-spin in Yang–Mills matrix models

Sperling

Steinacker

2019

Nuclear Physics B

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We consider the SO(4, 1)-covariant fuzzy hyperboloid H 4 n as a solution of Yang-Mills matrix models, and study the resulting higher-spin gauge theory. The degrees of freedom can be identified with functions on classical H 4 taking values in a higher-spin algebra associated to so(4, 1), truncated at spin n. We develop a suitable calculus to classify the higher-spin modes, and show that the tangential modes are stable. The metric fluctuations encode one of the spin 2 modes, however they do not propagate in the classical matrix model. Gravity is argued to arise upon taking into account induced gravity terms. This formalism can be applied to the cosmological FLRW space-time solutions of [1], which arise as projections of H 4 n . We establish a one-to-one correspondence between the tangential fluctuations of these spaces.

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“…One interesting outcome is that it may provide a interpretation for the UV/IR mixing for some noncommutative gauge theories in terms of an induced gravity action. See e.g [49,50].…”

Section: Jhep12(2015)045mentioning

confidence: 99%

Noncommutative gauge theories on ℝ λ 3 $$ {\mathrm{\mathbb{R}}}_{\uplambda}^3 $$ : perturbatively finite models

Géré

Jurić²,

Wallet

2015

J. High Energ. Phys.

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We show that natural noncommutative gauge theory models on R 3 λ can accommodate gauge invariant harmonic terms, thanks to the existence of a relationship between the center of R 3 λ and the components of the gauge invariant 1-form canonical connection. This latter object shows up naturally within the present noncommutative differential calculus. Restricting ourselves to positive actions with covariant coordinates as field variables, a suitable gauge-fixing leads to a family of matrix models with quartic interactions and kinetic operators with compact resolvent. Their perturbative behavior is then studied. We first compute the 2-point and 4-point functions at the one-loop order within a subfamily of these matrix models for which the interactions have a symmetric form. We find that the corresponding contributions are finite. We then extend this result to arbitrary order. We find that the amplitudes of the ribbon diagrams for the models of this subfamily are finite to all orders in perturbation. This result extends finally to any of the models of the whole family of matrix models obtained from the above gauge-fixing. The origin of this result is discussed. Finally, the existence of a particular model related to integrable hierarchies is indicated, for which the partition function is expressible as a product of ratios of determinants.

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

Cited by 15 publications

References 44 publications

Non-commutative geometry and matrix models

Non-commutative geometry and matrix models

The fuzzy 4-hyperboloid Hn4 and higher-spin in Yang–Mills matrix models

Noncommutative gauge theories on ℝ λ 3 $$ {\mathrm{\mathbb{R}}}_{\uplambda}^3 $$ : perturbatively finite models

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