We construct a tensor-matrix model which describes 3-dimensional (3D) Causal Dynamical Triangulation (CDT) of open-closed surface. Though the usual splitting interaction of a surface is not derived from the stochastic quantization procedure, it provides another interaction of IK-type, which becomes the sole quantum correction. Through the double scaling limit, it realizes CDT open-closed surface field theory including the IK-type interactions in the same condition with the closed surface CDT model. Further, we investigate the commutation relations of the generators, for surfaces with the lowest numbers of boundary loops, in the Fokker-Planck (FP) Hamiltonian. The generators seem to close in their commutation relations in our 3D model, differently from the 2D model, where the algebraic structure was not exact when commutators contain the generator of the open string edge.
We extend the 2 dimensional Causal Dynamical Triangulation (CDT) model from the usual model of closed string to the one of open-closed string. The matrix-vector model describing the loop gas model is modified so as to possess the nature of the CDT, i.e. the time foliation structure. Stochastic quantization method produces interactions of loop and line variables similar to those in the non-critical open-closed string field theories. By taking an appropriate scaling, we realize an extended model of the generalized CDT (GCDT), which keeps the causality in a broad sense.
By explicitly allowing for topology to change as a function of time, two-dimensional quantum gravity defined through causal dynamical triangulations gives rise to a new continuum string field theory. Within a matrix-model formulation we show that -- rather remarkably -- the associated sum over all genera can be performed in closed form, leading to a nonperturbative definition of CDT string field theory. We also obtain explicit formulas for the n-loop correlation functions. Our construction exhibits interesting parallels with previous, purely Euclidean treatments.
We construct a 2-dimensional Causal Dynamical Triangulation (CDT) model from a matrix model which represents the loop gas model of closed string. The target-space index is reinterpreted as time or geodesic distance. We apply stochastic quantization method to the model to obtain the Generalized CDT (GCDT), which has additional interaction of creating baby universe. If we take a specific scaling in continuum limit, we realize an extended GCDT model characterized by the non-critical string field theory.
We study spacetimes with a closed conformal Killing-Yano tensor. It is shown that the D-dimensional Kerr-NUT-de Sitter spacetime constructed by Chen-Lu-Pope is the only spacetime admitting a rank-2 closed conformal Killing-Yano tensor with a certain symmetry.
In this paper we provide the closed equations that satisfy two-point correlation functions of the rank 3 and 4 tensorial group field theory. The formulation of the present problem extends the method used by Grosse and Wulkenhaar in [arXiv 0909.1389] to the tensor case. Ward-Takahashi identities and Schwinger-Dyson equations are combined to establish a nonlinear integral equation for the two-point functions. In the 3D case the solution of this equation is given perturbatively at second order of the coupling constant.
A systematic method is presented for the construction and classification of algebras of gauge transformations for arbitrary high rank tensor gauge fields. For every tensor gauge field of a given rank, the gauge transformation will be stated, in a generic way, via an ansatz that contains all the possible terms, with arbitrary coefficients and the maximum number of tensor gauge functions. The requirement for the closure of the algebra will prove to be restrictive, but, nevertheless, leave a variety of choices. Properly adjusting the values of the initial coefficients and imposing restrictions on…
Assuming the existence of a single rank-2 closed conformal Killing-Yano tensor with a certain symmetry we show that there exist mutually commuting rank-2 Killing tensors and Killing vectors. We also discuss the condition of separation of variables for the geodesic Hamilton-Jacobi equations.
The higher-dimensional Kerr-NUT-de Sitter spacetime describes the general rotating asymptotically de Sitter black hole with NUT parameters. It is known that such a spacetime possesses a rank-2 closed conformal Killing-Yano (CKY) tensor as a ``hidden'' symmetry which provides the separation of variables for the geodesic equations and Klein-Gordon equations. We present a classification of higher-dimensional spacetimes admitting a rank-2 closed CKY tensor. This provides a generalization of the Kerr-NUT-de Sitter spacetime. In particular, we show that the Kerr-NUT-de Sitter spacetime is the only s…
We show that a U(1) gauge theory defined in the configuration space for closed p-branes yields the gauge theory of a massless rank-(p+1) antisymmetric tensor field and the Stueckelberg formalism for a massive vector field.
The energy-momentum tensor of Matrix Theory is derived by computing disk amplitudes with one closed string and an arbitrary number of open strings and by taking the DKPS limit. We clarify its relation to the energy-momentum tensor of the noncommutative gauge theory derived in our previous paper.
In string theory, higher rank antisymmetric tensor fields appear as massless excitations of closed strings. Till date there is no experimental support in favour of their existence. In a stringy framework, starting from a warped throat-like Klebanov-Strassler geometry, we show that all the massless higher rank antisymmetric tensor fields are heavily suppressed due to the background fluxes leading to their invisibility in our Universe.
We describe an accelerating universe model in the context of a scalar-tensor theory. This model is intrinsically closed, and is filled with quintessence-like scalar field components, in addition to the Cold Dark Matter component. With a background geometry specified by the Friedman-Robertson-Walker metric, we establish conditions under which this closed cosmological model, described in a scalar-tensor theory, may look flat in a genuine Jordan-Brans-Dicke theory. Both models become indistinguishable at low enough redshift.
We consider non-supersymmetric four-dimensional closed string theories constructed out of tensor products of N=2 minimal models. Generically such theories have closed string tachyons, but these may be removed either by choosing a non-trivial partition function or a suitable Klein bottle projection. We find large numbers of examples of both types.
We study the behavior of the scattering amplitudes of the bosonic string involving a soft massless state (graviton, dilaton and Kalb-Ramond antisymmetric tensor) and closed string tachyons or other closed string massless states. For a soft graviton we confirm the results, obtained in Ref. [24] using just gauge invariance, up to terms of ${\cal O}(q^1)$ for external tachyons and up to terms of ${\cal O} (q^0)$ for external massless closed string states. Furthermore, we also derive the behavior of the scattering amplitude when a dilaton or a Kalb-Ramond field becomes soft. These results are new …
The Kalb-Ramond action for an interacting string is generalized to the case of a high-dimensional object (p-brane). The interaction is found to be mediated by a gauge boson of a completely antisymmetric tensor of rank $p+1$.
In a recent paper [17], we studied the evolution of the background geometry and scalar perturbations in an inflationary, spatially closed Friedmann-Lemaître-Robertson-Walker (FLRW) model having constant positive spatial curvature and spatial topology $\mathbb S^3$. Due to the spatial curvature, the early phase of slow-roll inflation is modified, leading to suppression of power in the scalar power spectrum at large angular scales. In this paper, we extend the analysis to include tensor perturbations. We find that --- similarly to the scalar perturbations --- the tensor power spectrum also shows…
The BICEP-2 team has reported the detection of primordial cosmic microwave background B-mode polarization, with hints of a suppression of power at large angular scales relative to smaller scales. Provided that the B-mode polarization is due to primordial gravitational waves, this might imply a blue tilt of the primordial gravitational wave spectrum. Such a tilt would be incompatible with standard inflationary models, although it was predicted some years ago in the context of a mechanism that thermally generates the primordial perturbations through a Hagedorn phase of string cosmology. The purp…
We consider a $R^{1,d}/Z_2$ orbifold, where $Z_2$ acts by time and space reversal, also known as the embedding space of the elliptic de Sitter space. The background has two potentially dangerous problems: time-nonorientability and the existence of closed time-like curves. We first show that closed causal curves disappear after a proper definition of the time function. We then consider the one-loop vacuum expectation value of the stress tensor. A naive QFT analysis yields a divergent result. We then analyze the stress tensor in bosonic string theory, and find the same result as if the target sp…
We introduce the notions of open-closed field algebra and open-closed field algebra over a vertex operator algebra V. In the case that V satisfies certain finiteness and reductivity conditions, we show that an open-closed field algebra over V canonically gives an algebra over a $\C$-extension of the Swiss-cheese partial operad. We also give a tensor categorical formulation and categorical constructions of open-closed field algebras over V.
Gott spacetime has closed timelike curves, but no locally anomalous stress-energy. A complete orthonormal set of eigenfunctions of the wave operator is found in the special case of a spacetime in which the total deficit angle is $2π$. A scalar quantum field theory is constructed using these eigenfunctions. The resultant interacting quantum field theory is not unitary because the field operators can create real, on-shell, particles in the acausal region. These particles propagate for finite proper time accumulating an arbitrary phase before being annihilated at the same spacetime point as that …
We propose a time-varying parameter $\underlineα$ for Gödel metric and an energy momentum tensor corresponding to this geometry is found. To satisfy covariance arguments time-varying gravitational and cosmological term are introduced. The ``Einstein's equation'' for this special evolution for the Universe are written down where expansion, rotation and closed time-like curves appear as a combination between standard model, Gödel and steady state properties are obtained.
We solve the closed Schwinger-Dyson equation for the 2-point function of a tensor field theory with a quartic melonic interaction, in terms of Lambert's W-function, using a perturbative expansion and Lagrange-Bürmann resummation. Higher-point functions are then obtained recursively.
Let $V$ be a vertex operator algebra satisfying certain reductivity and finiteness conditions such that $\mathcal{C}_V$, the category of V-modules, is a modular tensor category. We study open-closed field algebras over V equipped with nondegenerate invariant bilinear forms for both open and closed sectors. We show that they give algebras over certain $\C$-extension of the Swiss-cheese partial dioperad, and we obtain Ishibashi states easily in such algebras. We formulate Cardy condition algebraically in terms of the action of the modular transformation $S: τ\mapsto -\frac{1}τ$ on the space of i…
We consider an initial condition problem in a nearly quadratic chaotic inflation model in supergravity. We introduce shift symmetry breaking not only in the superpotential but also in the Kahler potential. In this model the inflaton potential is nearly quadratic for inflaton field values around the Planck scale, but deviates from the quadratic one for larger field values. As a result, the prediction on the tensor-to-scalar ratio can be smaller than that of a purely quadratic model. Due to the shift symmetry breaking in the Kahler potential, the inflaton potential becomes steep for large inflat…
