Classical defects in higher-dimensional Einstein gravity coupled to nonlinear $$\sigma $$-models

We construct solutions of higher-dimensional Einstein gravity coupled to nonlinear \(\sigma \)-model with cosmological constant. The \(\sigma \)-model can be perceived as exterior configuration of a spontaneously-broken \(SO(D-1)\) global higher-codimensional “monopole”. Here we allow the kinetic term of the \(\sigma \)-model to be noncanonical; in particular we specifically study a quadratic-power-law type. This is some possible higher-dimensional generalization of the Bariola–Vilenkin (BV) solutions with k-global monopole studied recently. The solutions can be perceived as the exterior solution of a black hole swallowing up noncanonical global defects. Even in the absence of comological constant its surrounding spacetime is asymptotically non-flat; it suffers from deficit solid angle. We discuss the corresponding horizons. For \(\Lambda >0\) in 4d there can exist three extremal conditions (the cold, ultracold, and Nariai black holes), while in higher-than-four dimensions the extremal black hole is only Nariai. For \(\Lambda <0\) we only have black hole solutions with one horizon, save for the 4d case where there can exist two horizons. We give constraints on the mass and the symmetry-breaking scale for the existence of all the extremal cases. In addition, we also obtain factorized solutions, whose topology is the direct product of two-dimensional spaces of constant curvature (\(M_2\), \(dS_2\), or \(AdS_2\)) with (D-2)-sphere. We study all possible factorized channels.     

Inflation in SU(5) GUT models coupled to gravity

We have examined the SU(5) GUT phase transition in (nearly) Coleman-Weinberg type models coupled to gravity and have found three different modes through which the transition may proceed, depending upon the choice of (zero temperature) parameters. For each of these modes, we have determined numerically whether there is sufficient inflation to explain some long standing cosmological puzzles, and we find that this is the case only in a very restricted region of parameter space.     

Scaling in four-dimensional quantum gravity

We discuss scaling relations in four-dimensional simplicial quantum gravity. Using numerical results obtained with a new algorithm called “baby universe surgery” we study the critical region of the theory. The position of the phase transition is given with high accuracy and some critical exponents are measured. Their values prove that the transition is continuous. We discuss the properties of two distinct phases of the theory. For large values of the bare gravitational coupling constant the internal Hausdorff dimension is two (the elongated phase), and the continuum theory is that of so called branched polymers. For small values of the bare gravitational coupling constant the internal Hausdorff dimension seems to be infinite (the crumpled phase). We conjecture that this phase corresponds to a theory of topological gravity. At the transition point the Hausdorff dimension might be finite and larger than two. This transition point is a potential candidate for a non-perturbative theory of quantum gravity.     

A string-modified four-dimensional gravity theory

The route from string theory to a ten-dimensional supergravity/super-Yang-Mills field theory is briefly illumined. The process of extracting a classical four-dimensional gravity theory from the ten-dimensional theory is discussed and a simple model containing gravity, electromagnetism, a dilaton field, and a Kalb-Ramond field is proposed. The equations of motion of a test particle in a background of gravity, dilation, and Kalb-Ramond fields are displayed. Some static spherically symmetric vacuum solutions are derived, and some astrophysical implications are discussed.     

Inconsistencies in four-dimensional Einstein-Gauss-Bonnet gravity

We attempt to clarify several aspects concemi ng the recently presented four-dimensional Ein stein-Gauss-Bonnet gravity.We argue that the limiting procedure outlined in[Phys.Rev.Lett.124,081301(2020)]generally involves ill-defined terms in the four dimensional field equations.Potential ways to circumvent this issue are discussed,alongside remarks regarding specific solutions of the theory.We prove that,although linear perturbations are well behaved around maximally symmetric backgrounds,the equations for second-order perturbations are illdefined even around a Minkowskia n background.Additi on ally,we perform a detailed analysis of the spherically symmetric solutions and find that the central curvature singularity can be reached within a finite proper time.     

Pseudo-topological transitions in 2D gravity models coupled to massless scalar fields

We study the geometries generated by two-dimensional causal dynamical triangulations (CDT) coupled to d   massless scalar fields. Using methods similar to those used to study four-dimensional CDT we show that there exists a c=1$c=1$ “barrier”, analogous to the c=1$c=1$ barrier encountered in non-critical string theory, only the CDT transition is easier to be detected numerically. For d?1$d?1$ we observe time-translation invariance and geometries entirely governed by quantum fluctuations around the uniform toroidal topology put in by hand. For d>1$d>1$ the effective average geometry is no longer toroidal but “semiclassical” and spherical with Hausdorff dimension _dH=3$d_H=3$. In the d>1$d>1$ sector we study the time dependence of the semiclassical spatial volume distribution and show that the observed behavior is described by an effective mini-superspace action analogous to the actions found in the de Sitter phase of three- and four-dimensional pure CDT simulations and in the three-dimensional CDT-like Ho?ava–Lifshitz models.     

Cohomological analysis of bosonic D-strings and 2d sigma models coupled to abelian gauge fields

We analyze completely the BRST cohomology on local functionals for two-dimensional sigma models coupled to abelian world-sheet gauge fields, including effective bosonic D-string models described by Born-Infeld actions. In particular we prove that the rigid symmetries of such models are exhausted by the solutions to generalized Killing vector equations which we have presented recently, and provide all the consistent first order deformations and candidate gauge anomalies of the models under study. For appropriate target space geometries we find nontrivial deformations both of the abelian gauge transformations and of the world-sheet diffeomorphisms, and antifield-dependent candidate anomalies for both types of symmetries separately, as well as mixed ones.     

Asymptotic behavior and Hamiltonian analysis of anti-de Sitter gravity coupled to scalar fields

We examine anti-de Sitter gravity minimally coupled to a self-interacting scalar field in D ? 4 dimensions when the mass of the scalar field is in the range . Here, l is the AdS radius, and is the Breitenlohner-Freedman mass. We show that even though the scalar field generically has a slow fall-off at infinity which back reacts on the metric so as to modify its standard asymptotic behavior, one can still formulate asymptotic conditions (i) that are anti-de Sitter invariant; and (ii) that allows the construction of well-defined and finite Hamiltonian generators for all elements of the anti-de Sitter algebra. This requires imposing a functional relationship on the coefficients a, b that control the two independent terms in the asymptotic expansion of the scalar field. The anti-de Sitter charges are found to involve a scalar field contribution. Subtleties associated with the self-interactions of the scalar field as well as its gravitational back reaction, not discussed in previous treatments, are explicitly analyzed. In particular, it is shown that the fields develop extra logarithmic branches for specific values of the scalar field mass (in addition to the known logarithmic branch at the B-F bound).     

Algebraic approach to anomalous sigma models

Anomalous σ-models in 1+1 and 1+3 dimensions are analysed using purely algebraic methods. We find, in the 1+1 dimensional example, a current algebra containing an arbitrary parameter which is compatible with the Wess-Zumino anomaly and anon-vanishing curvature. The consistency of the algebra is checked by means of a consistency condition and the Jacobi identity. In the 1+3 dimensional case, however, the conventional (anomalous) current algebra with a vanishing curvature is reproduced.     

Topological sigma models

A variant of the usual supersymmetric nonlinear sigma model is described, governing maps from a Riemann surface to an arbitrary almost complex manifoldM. It possesses a fermionic BRST-like symmetry, conserved for arbitrary, and obeyingQ ²=0. In a suitable version, the quantum ground states are the 1+1 dimensional Floer groups. The correlation functions of the BRST-invariant operators are invariants (depending only on the homotopy type of the almost complex structure ofM) similar to those that have entered in recent work of Gromov on symplectic geometry. The model can be coupled to dynamical gravitational or gauge fields while preserving the fermionic symmetry; some observations by Atiyah suggest that the latter coupling may be related to the Jones polynomial of knot theory. From the point of view of string theory, the main novelty of this type of sigma model is that the graviton vertex operator is a BRST commutator. Thus, models of this type may correspond to a realization at the level of string theory of an unbroken phase of quantum gravity.On leave from Department of Physics, Princeton University. Supported in part by NSF Grants No. 80-19754, 86-16129, 86-20266