Publications (74)
Covariant Field Equations, Gauge Fields and Conservation Laws from Yang-Mills Matrix Models
Harold Steinacker
The effective geometry and the gravitational coupling of nonabelian gauge and scalar fields on generic NC branes in Yang-Mills matrix models is determined. Covariant field equation…
Emergent Gravity from Noncommutative Gauge Theory
Harold Steinacker
We show that the matrix-model action for noncommutative U(n) gauge theory actually describes SU(n) gauge theory coupled to gravity. This is elaborated in the 4-dimensional case. Th…
On the 1-loop effective action for the IKKT model and non-commutative branes
Daniel N. Blaschke, Harold Steinacker
We study the one-loop effective action of the IKKT or IIB model on a 4-dimensional non-commutative brane background. The trace-U(1) sector is governed by non-commutativity, and lea…
Propagator on the h-deformed Lobachevsky plane
John Madore, Harold Steinacker
The action of the isometry algebra U_h(sl(2)) on the h-deformed Lobachevsky plane is found. The invariant distance and the invariant 2-point functions are shown to agree precisely…
Exact renormalization of a noncommutative Ï^3 model in 6 dimensions
Harald Grosse, Harold Steinacker
The noncommutative selfdual Ï^3 model in 6 dimensions is quantized and essentially solved, by mapping it to the Kontsevich model. The model is shown to be renormalizable and asymp…
Matrix description of D-branes on 3-spheres
Jacek Pawelczyk, Harold Steinacker
We discuss a matrix model for D0-branes on S^3 \times M^7 based on quantum group symmetries. For finite radius of S^3 (i.e. for finite k), it gives results beyond the reach of the…
Noncommutative gauge theory and symmetry breaking in matrix models
Harald Grosse, Fedele Lizzi, Harold Steinacker
We show how the fields and particles of the standard model can be naturally realized in noncommutative gauge theory. Starting with a Yang-Mills matrix model in more than 4 dimensio…
Curvature and Gravity Actions for Matrix Models
Daniel N. Blaschke, Harold Steinacker
We show how gravitational actions, in particular the Einstein-Hilbert action, can be obtained from additional terms in Yang-Mills matrix models. This is consistent with recent resu…
Spatially flat FLRW spacetimes with a Big Bang from matrix geometry
Christian GaÃ, Harold Steinacker
We present an expanding, spatially flat () FLRW quantum spacetime with a Big Bang, considered as a background in Yang-Mills matrix models. The FLRW geometry emerges in the sem…
Integration on quantum Euclidean space and sphere in dimensions
Harold Steinacker
Invariant integrals of functions and forms over - deformed Euclidean space and spheres in dimensions are defined and shown to be positive definite, compatible with the star…
Algebraic brane dynamics on SU(2): excitation spectra
Jacek Pawelczyk, Harold Steinacker
We analyze the dynamics of D2-branes on SU(2) within a recently proposed matrix model, which works for finite radius of SU(2). The spectrum of single-brane excitations turns out to…
Fuzzy extra dimensions and particle physics models
Athanasios Chatzistavrakidis, Harold Steinacker, George Zoupanos
In the present contribution the construction of particle physics models in theories with fuzzy extra dimensions is discussed. We focus on a bottom-up approach where the structure o…
Nonabelian localization for gauge theory on the fuzzy sphere
Harold Steinacker, Richard J. Szabo
We apply nonabelian equivariant localization techniques to Yang-Mills theory on the fuzzy sphere to write the partition function entirely as a sum over local contributions from cri…
Quantization and eigenvalue distribution of noncommutative scalar field theory
Harold Steinacker
The quantization of noncommutative scalar field theory is studied from the matrix model point of view, exhibiting the significance of the eigenvalue distribution. This provides a n…
Finite Gauge Theory on Fuzzy CP^2
Harald Grosse, Harold Steinacker
We give a non-perturbative definition of U(n) gauge theory on fuzzy CP^2 as a multi-matrix model. The degrees of freedom are 8 hermitian matrices of finite size, 4 of which are tan…
Split noncommutativity and compactified brane solutions in matrix models
Harold Steinacker
Solutions of the undeformed IKKT matrix model with structure R^{3,1} x K are presented, where the noncommutativity relates the compact with the non-compact space. The extra dimensi…
Gauge Theory on Fuzzy S^2 x S^2 and Regularization on Noncommutative R^4
Wolfgang Behr, Frank Meyer, Harold Steinacker
We define U(n) gauge theory on fuzzy S^2_N x S^2_N as a multi-matrix model, which reduces to ordinary Yang-Mills theory on S^2 x S^2 in the commutative limit N -> infinity. The mod…
Fermions Coupled to Emergent Noncommutative Gravity
Daniela Klammer, Harold Steinacker
We study the coupling of fermions to Yang-Mills matrix models in the framework of emergent noncommutative gravity. It is shown that the matrix model action provides an appropriate…
Emergent Gravity, Matrix Models and UV/IR Mixing
Harald Grosse, Harold Steinacker, Michael Wohlgenannt
We verify explicitly that UV/IR mixing for noncommutative gauge theory can be understood in terms of an induced gravity action, as predicted by the identification [1] of gravity wi…
Spinorial higher-spin gauge theory from IKKT in Euclidean and Minkowski signatures
Harold Steinacker, Tung Tran
We explore the semi-classical relation between the fuzzy 4-hyperboloid and non-compact quantized twistor space at large . This provides two background…
Quantum Anti-de Sitter space and sphere at roots of unity
Harold Steinacker
An algebra of functions on q-deformed Anti-de Sitter space AdS_q^D is defined which is covariant under U_q(so(2,D-1)), for q a root of unity. The star-structure is studied in detai…
A quantum algebraic description of D-branes on group manifolds
Jacek Pawelczyk, Harold Steinacker
We propose an algebraic description of (untwisted) D-branes on compact group manifolds using quantum algebras related to $U_q(\mg)$. It reproduces the known characteristics of…
Generalized Fuzzy Torus and its Modular Properties
Paul Schreivogl, Harold Steinacker
We consider a generalization of the basic fuzzy torus to a fuzzy torus with non-trivial modular parameter, based on a finite matrix algebra. We discuss the modular properties of th…
Gauge Theory on the Fuzzy Sphere and Random Matrices
Harold Steinacker
This is a short version of hep-th/0307075, describing the formulation of Yang-Mills theory on the fuzzy sphere as multi-matrix model, its monopole solutions and the quantization us…
Non-commutative geometry and matrix models
Harold Steinacker
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…
Orbifold matrix models and fuzzy extra dimensions
Athanasios Chatzistavrakidis, Harold Steinacker, George Zoupanos
We revisit an orbifold matrix model obtained as a restriction of the type IIB matrix model on a Z_3-invariant sector. An investigation of its moduli space of vacua is performed and…
2D fuzzy Anti-de Sitter space from matrix models
Danijel Jurman, Harold Steinacker
We study the fuzzy hyperboloids AdS^2 and dS^2 as brane solutions in matrix models. The unitary representations of SO(2,1) required for quantum field theory are identified, and exp…
Unbraiding the braided tensor product
Gaetano Fiore, Harold Steinacker, Julius Wess
We show that the braided tensor product algebra of two module algebras of a quasitriangular Hopf algebra is equal to the ordinary tensor…
Quantized Gauge Theory on the Fuzzy Sphere as Random Matrix Model
Harold Steinacker
U(n) Yang-Mills theory on the fuzzy sphere S^2_N is quantized using random matrix methods. The gauge theory is formulated as a matrix model for a single Hermitian matrix subject to…
Field Theory on the q-deformed Fuzzy Sphere I
Harald Grosse, John Madore, Harold Steinacker
We study the q-deformed fuzzy sphere, which is related to D-branes on SU(2) WZW models, for both real q and q a root of unity. We construct for both cases a differential calculus w…
Fermions on spontaneously generated spherical extra dimensions
Harold Steinacker, George Zoupanos
We include fermions to the model proposed in hep-th/0606021, and obtain a renormalizable 4-dimensional SU(N) gauge theory which spontaneously generates fuzzy extra dimensions and b…
Quantum Groups, Roots of Unity and Particles on quantized Anti-de Sitter Space
Harold Steinacker
Quantum groups in general and the quantum Anti-de Sitter group in particular are studied from the point of view of quantum field theory. We show that if is a sui…
Curvature and Gravity Actions for Matrix Models II: the case of general Poisson structure
Daniel N. Blaschke, Harold Steinacker
We study the geometrical meaning of higher-order terms in matrix models of Yang-Mills type in the semi-classical limit, generalizing recent results arXiv:1003.4132 to the case of 4…
Emergent 4D Gravity from Matrix Models
Harold Steinacker
Recent progress in the understanding of gravity on noncommutative spaces is discussed. A gravity theory naturally emerges from matrix models of noncommutative gauge theory. The eff…
Brane compactifications and 4-dimensional geometry in the IKKT model
Alexios P. Polychronakos, Harold Steinacker, Jochen Zahn
We study in detail certain brane solutions with compact extra dimensions M^4 x K in the IKKT matrix model, with K being a two-dimensional rotating torus embedded in R^6. We focus o…
The curvature of branes, currents and gravity in matrix models
Harold Steinacker
The curvature of brane solutions in Yang-Mills matrix models is expressed in terms of conserved currents associated with global symmetries of the model. This implies a relation bet…
Heat kernel expansion and induced action for the matrix model Dirac operator
Daniel N. Blaschke, Harold Steinacker, Michael Wohlgenannt
We compute the quantum effective action induced by integrating out fermions in Yang-Mills matrix models on a 4-dimensional background, expanded in powers of a gauge-invariant UV cu…
Emergent Gravity and Noncommutative Branes from Yang-Mills Matrix Models
Harold Steinacker
The framework of emergent gravity arising from Yang-Mills matrix models is developed further, for general noncommutative branes embedded in R^D. The effective metric on the brane t…
Emergent Geometry and Gravity from Matrix Models: an Introduction
Harold Steinacker
A introductory review to emergent noncommutative gravity within Yang-Mills Matrix models is presented. Space-time is described as a noncommutative brane solution of the matrix mode…
On the fermion spectrum of spontaneously generated fuzzy extra dimensions with fluxes
Athanasios Chatzistavrakidis, Harold Steinacker, George Zoupanos
We consider certain vacua of four-dimensional SU(N) gauge theory with the same field content as the N=4 supersymmetric Yang-Mills theory, resulting from potentials which break the…
On the Newtonian limit of emergent NC gravity and long-distance corrections
Harold Steinacker
We show how Newtonian gravity emerges on 4-dimensional non-commutative spacetime branes in Yang-Mills matrix models. Large matter clusters such as galaxies are embedded in large-sc…
Cosmological solutions of emergent noncommutative gravity
Daniela Klammer, Harold Steinacker
Matrix models of Yang-Mills type lead to an emergent gravity theory, which may not require fine-tuning of a cosmological constant. We find cosmological solutions of Friedmann-Rober…
Orbifolds, fuzzy spheres and chiral fermions
Athanasios Chatzistavrakidis, Harold Steinacker, George Zoupanos
Starting with a N=4 supersymmetric Yang-Mills theory in four dimensions with gauge group SU(3N) we perform an orbifold projection leading to a N=1 supersymmetric SU(N)^3 Yang-Mills…
An Index for Intersecting Branes in Matrix Models
Harold Steinacker, Jochen Zahn
We introduce an index indicating the occurrence of chiral fermions at the intersection of branes in matrix models. This allows to discuss the stability of chiral fermions under per…
Monopole Bundles over Fuzzy Complex Projective Spaces
Ursula Carow-Watamura, Harold Steinacker, Satoshi Watamura
We give a construction of the monopole bundles over fuzzy complex projective spaces as projective modules. The corresponding Chern classes are calculated. They reduce to the monopo…
Matrix Models, Emergent Spacetime and Symmetry Breaking
Harald Grosse, Fedele Lizzi, Harold Steinacker
We discuss how a matrix model recently shown to describe emergent gravity may contain extra degrees of freedom which reproduce some characteristics of the standard model, in partic…
Fuzzy Instantons
Harald Grosse, Marco Maceda, John Madore +1
We present a series of instanton-like solutions to a matrix model which satisfy a self-duality condition and possess an action whose value is, to within a fixed constant factor, an…
Twisted WZW Branes from Twisted REA's
Jacek Pawelczyk, Harold Steinacker, Rafal R. Suszek
Quantum geometry of twisted Wess--Zumino--Witten branes is formulated in the framework of twisted Reflection Equation Algebras. It is demonstrated how the representation theory of…
Quantum Cognition Machine Learning for Forecasting Chromosomal Instability
Giuseppe Di Caro, Vahagn Kirakosyan, Alexander G. Abanov +11
The accurate prediction of chromosomal instability from the morphology of circulating tumor cells (CTCs) enables real-time detection of CTCs with high metastatic potential in the c…
A non-perturbative approach to non-commutative scalar field theory
Harold Steinacker
Non-commutative Euclidean scalar field theory is shown to have an eigenvalue sector which is dominated by a well-defined eigenvalue density, and can be described by a matrix model.…
Aspects of the q-deformed Fuzzy Sphere
Harold Steinacker
These notes are a short review of the q-deformed fuzzy sphere S^2_{q,N}, which is a ``finite'' noncommutative 2-sphere covariant under the quantum group U_q(su(2)). We discuss its…
Decoupling Braided Tensor Factors
Gaetano Fiore, Harold Steinacker, Julius Wess
We briefly report on our result that the braided tensor product algebra of two module algebras of a quasitriangular Hopf algebra is equal to the ordinary tensor produ…
Gauge Field Theory on the E_q(2)-covariant Plane
Frank Meyer, Harold Steinacker
Gauge theory on the q-deformed two-dimensional Euclidean plane R^2_q is studied using two different approaches. We first formulate the theory using the natural algebraic structures…
Quantum Anti-de Sitter Space at Roots of Unity
Harold Steinacker
This is a short summary of the paper hep-th/9910037. An algebra of functions on q-deformed Anti-de Sitter space AdS_q^D is defined for q a root of unity, which is covariant under U…
Field theoretic models on covariant quantum spaces
Harold Steinacker
This thesis is based on hep-th/0203110, hep-th/0005273, hep-th/0107068, hep-th/0106205, and hep-th/0103164, but includes additional results, details, and background material. It co…
q-deformed Dirac Monopole With Arbitrary Charge
Chong-Sun Chu, Pei-Ming Ho, Harold Steinacker
We construct the deformed Dirac monopole on the quantum sphere for arbitrary charge using two different methods and show that it is a quantum principal bundle in the sense of Brzez…
Gauge Symmetry Breaking in Matrix Models
Harald Grosse, Fedele Lizzi, Harold Steinacker
We argue that some features of the standard model, in particular the fermion assignment and symmetry breaking, can be obtained in matrix model which describes noncommutative gauge…
Finite dimensional unitary representations of quantum Anti-de Sitter groups at roots of unity
Harold Steinacker
We study irreducible unitary \reps of and for a root of unity, which are finite dimensional. Among others, unitary \reps corresponding to all clas…
Fermions and Emergent Noncommutative Gravity
Daniela Klammer, Harold Steinacker
Fermions coupled to Yang-Mills matrix models are studied from the point of view of emergent gravity. We show that the simple matrix model action provides an appropriate coupling fo…
Gravity and compactified branes in matrix models
Harold Steinacker
A mechanism for emergent gravity on brane solutions in Yang-Mills matrix models is exhibited. Newtonian gravity and a partial relation between the Einstein tensor and the energy-mo…
Localization for Yang-Mills Theory on the Fuzzy Sphere
Harold Steinacker, Richard J. Szabo
We present a new model for Yang-Mills theory on the fuzzy sphere in which the configuration space of gauge fields is given by a coadjoint orbit. In the classical limit it reduces t…
Scaling Limits of the Fuzzy Sphere at one Loop
Chong-Sun Chu, John Madore, Harold Steinacker
We study the one loop dynamics of QFT on the fuzzy sphere and calculate the planar and nonplanar contributions to the two point function at one loop. We show that there is no UV/IR…
On Poisson geometries related to noncommutative emergent gravity
Nikolaj Kuntner, Harold Steinacker
We study metric-compatible Poisson structures in the semi-classical limit of noncommutative emergent gravity. Space-time is realized as quantized symplectic submanifold embedded in…
Dynamical generation of fuzzy extra dimensions, dimensional reduction and symmetry breaking
Paolo Aschieri, Theodoros Grammatikopoulos, Harold Steinacker +1
We present a renormalizable 4-dimensional SU(N) gauge theory with a suitable multiplet of scalar fields, which dynamically develops extra dimensions in the form of a fuzzy sphere S…
Intersecting branes and a standard model realization in matrix models
Athanasios Chatzistavrakidis, Harold Steinacker, George Zoupanos
We consider intersecting brane solutions of the type IIB matrix model. It is shown that fermionic zero-modes arise on such backgrounds, localized at the brane intersections. They l…
On matrix geometry
Harold Steinacker
The foundations of matrix geometry are discussed, which provides the basis for recent progress on the effective geometry and gravity in Yang-Mills matrix models. Basic examples lea…
Convergent Perturbation Theory for a q-deformed Anharmonic Oscillator
Rainer Dick, Andrea Pollok-Narayanan, Harold Steinacker +1
A --deformed anharmonic oscillator is defined within the framework of --deformed quantum mechanics. It is shown that the Rayleigh--Schrödinger perturbation series for the bo…
Matrix Models, Emergent Gravity, and Gauge Theory
Harold Steinacker
Matrix models of Yang-Mills type induce an effective gravity theory on 4-dimensional branes, which are considered as models for dynamical space-time. We review recent progress in t…
Unitary Representations of Noncompact Quantum Groups at Roots of Unity
Harold Steinacker
Noncompact forms of the Drinfeld-Jimbo quantum groups U_q(g) with (H_i)* = H_i, (X_i^{+-})* = s_i X_i^{-+} for s_i= +-1 are studied at roots of unity. This covers g = so(n,2p), su(…
Fermions and noncommutative emergent gravity II: Curved branes in extra dimensions
Daniela Klammer, Harold Steinacker
We study fermions coupled to Yang-Mills matrix models from the point of view of emergent gravity. The matrix model Dirac operator provides an appropriate coupling for fermions to t…
Unitary Representations and BRST Structure of the Quantum Anti--de Sitter Group at Roots of Unity
Harold Steinacker
It is shown that for suitable roots of unity, there exist finite--dimensional unitary representations of corresponding to all classical one-particle representations…
Schwarzschild Geometry Emerging from Matrix Models
Daniel N. Blaschke, Harold Steinacker
We demonstrate how various geometries can emerge from Yang-Mills type matrix models with branes, and consider the examples of Schwarzschild and Reissner-Nordstroem geometry. We pro…
Noncommutative Gauge Theory on the q-Deformed Euclidean Plane
Frank Meyer, Harold Steinacker
In this talk we recall some concepts of Noncommutative Gauge Theories. In particular, we discuss the q-deformed two-dimensional Euclidean Plane which is covariant with respect to t…
A Twistorial Description of the IKKT-Matrix Model
Harold Steinacker, Tung Tran
We consider the fuzzy 4-sphere as a background in the IKKT matrix model and explore the relation between and fuzzy twistor space in the semi-classical limit. A nove…