A. Ballesteros, I. Gutierrez-Sagredo, F.J. Herranz

The space of time-like geodesics on Minkowski spacetime is constructed as a coset space of the Poincaré group in (3+1) dimensions with respect to the stabilizer of a worldline. When this homogeneous space is endowed with a Poisson homogeneous structure compatible with a given Poisson-Lie Poincaré group, the quantization of this Poisson bracket gives rise […]

Marcus Sperling, Harold C. Steinacker

We discuss a (3+1)-dimensional covariant quantum space-time describing a FLRW cosmology with Big Bounce, obtained by a projection of the fuzzy hyperboloid H4n. This provides a background solution of the IKKT matrix model with mass term. We characterize the bosonic fluctuation spectrum, which consists of a tower of higher-spin modes, truncated at n. The modes […]

A. Ballesteros, I. Gutierrez-Sagredo, F.J. Herranz

The eight nonisomorphic Drinfel’d double (DD) structures for the Poincaré Lie group in (2+1) dimensions are explicitly constructed in the kinematical basis. Also, the two existing DD structures for a non-trivial central extension of the (1+1) Poincaré group are also identified and constructed, while in (3+1) dimensions no Poincaré DD structure does exist. Each of […]

A. Ballesteros, F. Mercati

We study the Lie bialgebra structures that can be built on the one-dimensional central extension of the Poincaré and (A)dS algebras in (1+1) dimensions. These central extensions admit more than one interpretation, but the simplest one is that they describe the symmetries of (the noncommutative deformation of) an Abelian gauge theory, $U(1)$ or $SO(2)$ on […]

Marcus Sperling, Harold C. Steinacker

We consider the SO(4,1)-covariant fuzzy hyperboloid H4n 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 H4 taking values in a higher-spin algebra associated to (4,1), truncated at spin n. We develop a suitable calculus to classify the higher-spin […]

A. Ballesteros, G. Gubitosi, I. Gutierrez-Sagredo, F.J. Herranz

Curved momentum spaces associated to the $\kappa$-deformation of the (3+1) de Sitter and Anti-de Sitter algebras are constructed as orbits of suitable actions of the dual Poisson-Lie group associated to the $\kappa$-deformation with non-vanishing cosmological constant. The $\kappa$-de Sitter and $\kappa$-Anti-de Sitter curved momentum spaces are separately analysed, and they turn out to be, respectively, […]

Brian P Dolan

Geometrically the phase space of a mechanical system involves the co-tangent bundle of the configuration space. The phase space of a relativistic field theory is infinite dimensional and can be endowed with a symplectic structure defined in a perfectly co-variant manner that is very useful for discussing symmetries and conserved quantities of the system. In […]

Brian P Dolan

For a field theory that is invariant under diffeomorphisms there is a subtle interplay between symmetries, conservation laws and the phase space of the theory. The natural language for describing these ideas is that of differential forms and both differential forms on space-time and differential forms on the infinite dimensional space of solutions of the […]

Marcus Sperling, Harold C. Steinacker

We consider SU(N) N=4 super Yang-Mills with cubic and quadratic soft SUSY breaking potential, such that the global SU(4)R is broken to SU(3) or further. As shown recently, this set-up supports a rich set of non-trivial vacua with the geometry of self-intersecting SU(3) branes in 6 extra dimensions. The zero modes on these branes can […]

S. Gonzalez-Martin and C.P. Martin

We compute the lowest order gravitational UV divergent radiative corrections to the S matrix element of the fermion + fermion → fermion + fermion scattering process in the massive Yukawa theory, coupled either to Unimodular Gravity or to General Relativity. We show that both Unimodular Gravity and General Relativity give rise to the same UV […]

Aybike Catal-Ozer

We obtain massive deformations of Type IIA supergravity theory through duality twisted reductions of Double Field Theory (DFT) of massless Type II strings. The mass deformation is induced through the reduction of the DFT of the RR sector. Such reductions are determined by a twist element belonging to Spin+(10,10), which is the duality group of […]

S. Gonzalez-Martin and C. P. Martin

We work out the one-loop and order κ2 m2 UV divergent contributions, coming from Unimodular Gravity and General Relativity, to the S matrix element of the scattering process + → + in a λ 4 theory with mass m. We show that both Unimodular Gravity and General Relativity give rise to the same UV divergent contributions in Dimensional Regularization. […]

A. Ballesteros, N.R. Bruno, F.J. Herranz

The $\kappa$-deformation of the (2+1)D anti-de Sitter, Poincaré and de Sitter groups is presented through a unified approach in which the curvature of the spacetime (or the cosmological constant) is considered as an explicit parameter. The Drinfel’d-double and the Poisson-Lie structure underlying the $\kappa$-deformation are explicitly given, and the three quantum kinematical groups are obtained […]

Harold C. Steinacker

We present simple solutions of IKKT-type matrix models describing a quantized homogeneous and isotropic cosmology with k=−1, finite density of microstates and a resolved Big Bang. At late times, a linear coasting cosmology a(t)∝t is obtained, which is remarkably close to observation. The solution consists of two sheets with opposite intrinsic chiralities, which are connected […]

Harold C. Steinacker

We present simple solutions of IKKT-type matrix models describing quantized homogeneous and isotropic cosmologies, with finite density of microstates and a regular Big Bang (BB). The BB arises from a signature change of the effective metric on a fuzzy brane embedded in Lorentzian target space, in the presence of a quantized 4-volume form. The Hubble […]

Aybike Catal-Ozer

We study duality twisted reductions of the Double Field Theory (DFT) of the RR sector of massless Type II theory, with twists belonging to the duality group Spin+(10,10). We determine the action and the gauge algebra of the resulting theory and determine the conditions for consistency. In doing this, we work with the DFT action […]

S. Gonzalez-Martin and C.P. Martin

We study the beta functions of the quartic and Yukawa couplings of General Relativity and Unimodular Gravity coupled to the λφ^4 and Yukawa theories with masses. We show that the General Relativity corrections to those beta functions as obtained from the 1PI functional by using the standard MS multiplicative renormalization scheme of Dimensional Regularization are […]

Angel Ballesteros, Catherine Meusburger, Pedro Naranjo

The correspondence between Poisson homogeneous spaces over a Poisson-Lie group $G$ and Lagrangian Lie subalgebras of the classical double $D({\mathfrak g})$ is revisited and explored in detail for the case in which ${\mathfrak g}=D(\mathfrak a)$ is a classical double itself. We apply these results to give an explicit description of some coisotropic 2d Poisson homogeneous […]

A. Ballesteros, G. Gubitosi, I. Gutierrez-Sagredo, F.J. Herranz

We bring the concept that quantum symmetries describe theories with nontrivial momentum space properties one step further, looking at quantum symmetries of spacetime in presence of a nonvanishing cosmological constant $\Lambda$. In particular, the momentum space associated to the $\kappa$-deformation of the de Sitter algebra in (1+1) and (2+1) dimensions is explicitly constructed as a […]

Carmelo P. Martin

We work out the one-loop contribution to the lepton anomalous mag- netic moment coming from Unimodular Gravity. We use Dimen- sional Regularization and Dimensional Reduction to carry out the com- putations. In either case, we find that Unimodular Gravity gives rise to the same one-loop correction as that of General Relativity.

Marcus Sperling and Harold C. Steinacker

We examine in detail the higher spin fields which arise on the basic fuzzy sphere S4N in the semi-classical limit. The space of functions can be identified with functions on classical S4 taking values in a higher spin algebra associated to (5). Yang-Mills matrix models naturally provide an action formulation for higher spin gauge theory […]

Kazuyuki Furuuchi, Marcus Sperling

We study quantum tunnelling in Dante’s Inferno model of large field inflation. Such a tunnelling process, which will terminate inflation, becomes problematic if the tunnelling rate is rapid compared to the Hubble time scale at the time of inflation. Consequently, we constrain the parameter space of Dante’s Inferno model by demanding a suppressed tunnelling rate […]

Marcus Sperling and Harold C. Steinacker

We study in detail generalized 4-dimensional fuzzy spheres with twisted extra dimensions. These spheres can be viewed as SO(5)-equivariant projections of quantized coadjoint orbits of SO(6). We show that they arise as solutions in Yang-Mills matrix models, which naturally leads to higher-spin gauge theories on S4. Several types of embeddings in matrix models are found, […]

A. S. Cattaneo and A. Perez

We show that the non-Abelian nature of geometric fluxes - the corner-stone in the definition of quantum geometry in the framework of loop quantum gravity (LQG) - follows directly form the continuum canonical commutations relations of gravity in connection variables and the validity of the Gauss law. The present treatment simplifies previous formulations and thus […]

A. S. Cattaneo and M. Schiavina

This note describes the restoration of time in one-dimensional parameterization-invariant (hence timeless) models, namely the classically-equivalent Jacobi action and gravity coupled to matter. It also serves as a timely introduction by examples to the classical and quantum BV-BFV formalism as well as to the AKSZ method.

Enrique Álvarez, Sergio González-Martín, Carmelo P. Martín

The maximally helicity violating tree-level scattering amplitudes involving three, four or five gravitons are worked out in Unimodular Gravity. They are found to coincide with the corresponding amplitudes in General Relativity. This a remarkable result, insofar as both the propagators and the vertices are quite different in the two theories.

Catherine Meusburger

We prove that Kitaev’s lattice model for a finite-dimensional semisimple Hopf algebra H is equivalent to the combinatorial quantisation of Chern-Simons theory for the Drinfeld double D(H). This shows that Kitaev models are a special case of the older and more general combinatorial models. This equivalence is an analogue of the relation between Turaev-Viro and […]

Enrique Álvarez, Sergio González-Martín, Carmelo P. Martín

The symmetries of unimodular gravity are clarified somewhat.

H. C. Steinacker

We study perturbations of the 4-dimensional fuzzy sphere as a background in the IKKT or IIB matrix model. The linearized 4-dimensional Einstein equations are shown to arise from the classical matrix model action, without adding an Einstein-Hilbert term. The excitation modes with lowest spin are identified as gauge fields, metric and connection fields. In addition […]

H. C. Steinacker

Refining previous work by Iso, Kawai and Kitazawa, we discuss bi-local string states as a tool for loop computations in noncommutative field theory and matrix models. Defined in terms of coherent states, they exhibit the stringy features of noncommutative field theory. This leads to a closed form for the 1-loop effective action in position space, […]

Brian P Dolan

The equation of state associated with ${\cal N}=4$ supersymmetric Yang-Mills in 4 dimensions, for $SU(N)$ in the large $N$ limit, is investigated using the AdS/CFT correspondence. An asymptotically AdS black-hole on the gravity side provides a thermal background for the Yang-Mills theory on the boundary in which the cosmological constant is equivalent to a volume. […]

Tamás F. Görbe

We use Hamiltonian reduction to simplify Falqui and Mencattini’s recent proof of Sklyanin’s expression providing spectral Darboux coordinates of the rational Calogero-Moser system. This viewpoint enables us to verify a conjecture of Falqui and Mencattini, and to obtain Sklyanin’s formula as a corollary.

Enrique Álvarez, Sergio González-Martín, and Carmelo P. Martín

When quantizing conformal dilaton gravity, there is a conformal anomaly which starts at two-loop order. This anomaly stems from evanescent operators on the divergent parts of the effective action. The general form of the finite counterterm, which is necessary in order to insure cancellation of the Weyl anomaly to every order in perturbation theory, has […]

Nils Carqueville, Catherine Meusburger, Gregor Schaumann

We initiate a systematic study of 3-dimensional `defect’ topologi- cal quantum field theories, that we introduce as symmetric monoidal functors on stratified and decorated bordisms. For every such functor we construct a tricategory with duals, which is the natural categori- cation of a pivotal bicategory. This captures the algebraic essence of defect TQFTs, and it […]

E.I. Guendelman, E. Nissimov and S. Pacheva

We consider a modified gravity plus single scalar-field model, where the scalar Lagrangian couples symmetrically both to the standard Riemannian volume-form (spacetime integration measure density) given by the square-root of the determinant of the Riemannian metric, as well as to another non-Riemannian volume-form in terms of an auxiliary maximal-rank antisymmetric tensor gauge field. The pertinent […]

Fernando Ruiz Ruiz

Perturbative quantization of Yang-Mills theory with a gauge algebra given by the classical double of a semisimple Lie algebra is considered. The classical double of a real Lie algebra is a nonsemisimple real Lie algebra that admits a nonpositive definite invariant metric, the indefiniteness of the metric suggesting an apparent lack of unitarity. It is […]

L. Schneiderbauer and H. C. Steinacker

We develop a systematic approach to determine and measure numerically the geometry of generic quantum or “fuzzy” geometries realized by a set of finite-dimensional hermitian matrices. The method is designed to recover the semi-classical limit of quantized symplectic spaces embedded in ℝd including the well-known examples of fuzzy spaces, but it applies much more generally. […]

A. S. Cattaneo and M. Schiavina

The present paper shows that general relativity in the Arnowitt-Deser-Misner formalism admits a BV-BFV formulation. More precisely, for any d+1≠2 (pseudo-) Riemannian manifold M with space-like or time-like boundary components, the BV data on the bulk induces compatible BFV data on the boundary. As a byproduct, the usual canonical formulation of general relativity is recovered […]

Catherine Meusburger, Derek K. Wise

Hopf algebra gauge theory on a ribbon graph We generalise the notion of a group gauge theory on a graph embedded into an oriented surface to finite-dimensional ribbon Hopf algebras. By linearising the corresponding structures for groups, we obtain axioms that encode the notions of connections, the algebra of functions on connections, gauge transformations and […]

Harold C. Steinacker

We describe a stabilization mechanism for fuzzy $S^4_N$ in the Euclidean IIB matrix model in the presence of a positive mass term. The one-loop effective potential for the radius contains an attractive contribution attributed to supergravity, while the mass term induces a repulsive contribution for small radius due to SUSY breaking. This leads to a […]

Enrique Álvarez, Sergio González-Martín, Mario Herrero-Valeaand Carmelo P. Martín

Athanasios Chatzistavrakidis

n this paper we study the structure of the phase space in noncommutative geometry in the presence of a nontrivial frame. Our basic assumptions are that the underlying space is a symplectic and parallelizable manifold. Furthermore, we assume the validity of the Leibniz rule and the Jacobi identities. We consider noncommutative spaces due to the […]

Athanasios Chatzistavrakidis and Fridrik Freyr Gautason

Non-abelian gauge theories in the context of generalized complex geometry are discussed. The generalized connection naturally contains standard gauge and scalar fields, unified in a purely geometric way. We define the corresponding Yang-Mills theory on particular subbundles of a Courant algebroid, known as Dirac structures, where the generalized curvature is a tensor. Different Dirac structures […]

Athanasios Chatzistavrakidis

It is shown that a matrix model with SO(d,d) global symmetry is derived from a generalized Yang-Mills theory on the standard Courant algebroid. This model keeps all the positive features of the well-studied type IIB matrix model, and it has many additional welcome properties. We show that it does not only capture the dynamics of […]

Athanasios Chatzistavrakidis, Larisa Jonke and Olaf Lechtenfeld

The existence of genuinely non-geometric backgrounds, i.e. ones without geometric dual, is an important question in string theory. In this paper we examine this question from a sigma model perspective. First we construct a particular class of Courant algebroids as protobialgebroids with all types of geometric and non-geometric fluxes. For such structures we apply the […]

Athanasios Chatzistavrakidis, Andreas Deser and Larisa Jonke

Target space duality is one of the most profound properties of string theory. However it customarily requires that the background fields satisfy certain invariance conditions in order to perform it consistently; for instance the vector fields along the directions that T-duality is performed have to generate isometries. In the present paper we examine in detail […]

Fabrizio Canfora, Maxim Kurkov, Luigi Rosa, Patrizia Vitale

It is shown that in the noncommutative version of QED (NCQED) Gribov copies induced by the noncommutativity of space-time appear in the Landau gauge. This is a genuine effect of noncommutative geometry which disappears when the noncommutative parameter vanishes.

A. S. Cattaneo, M. Schiavina

The present paper shows that general relativity in the Arnowitt-Deser-Misner formalism admits a BV-BFV formulation. More precisely, for any d+1≠2 (pseudo-) Riemannian manifold M with space-like or time-like boundary components, the BV data on the bulk induces compatible BFV data on the boundary. As a byproduct, the usual canonical formulation of general relativity is recovered […]

A. Ballesteros, I. Gutierrez-Sagredo, F.J. Herranz, C. Meusburger, P. Naranjo

Noncommutative spacetimes are widely believed to model some properties of the quantum structure of spacetime at the Planck regime. In this contribution the construction of (anti-)de Sitter noncommutative spacetimes obtained through quantum groups is reviewed. In this approach the quantum deformation parameter $z$ is related to a Planck scale, and the cosmological constant $\Lambda$ plays […]

I. Gutierrez-Sagredo, A. Ballesteros, F.J. Herranz

All non-isomorphic three-dimensional Poisson homogeneous Euclidean spaces are constructed and analyzed, based on the classification of coboundary Lie bialgebra structures of the Euclidean group in 3-dimensions, and the only Drinfel’d double structure for this group is explicitly given. The similar construction for the Poincaré case is reviewed and the striking differences between the Lorentzian and […]