Large mass expansion of the one-loop effective action induced by a scalar field on the two-dimensional Minkowski background with non-trivial $(1+1)$ splitting
A large mass expansion of the one-loop effective action of a scalar field on the two-dimensional Minkowski spacetime is found in the system of coordinates, where the metric $g_{μν}(t,x)\neqη_{μν}=diag(1,-1)$, and $g_{μν}(t,x)$ tends to $η_{μν}$ at the spatial and temporal infinities. It is shown that, apart from the Coleman-Weinberg potential, this expansion contains the terms both analytic and non-analytic in $m^{-2}$, where $m$ is the mass of a scalar field. A general unambiguous expression for the one-loop correction to the effective action on non-stationary backgrounds is derived.
Boosted and rotated tetrad backgrounds for the Minkowski space are studied in $f(T)$ gravity. We perform Lorentzian perturbations at first order around non-trivial backgrounds and show that some Lorentz modes can exhibit non-trivial dynamics and can propagate in time. This remarkable feature gives evidence of additional mode(s) in the Lorentzian sector which have no precedent in Lorentz-violating modified gravities, however they can cast doubts onto even theoretical viability of these models.
Non-extreme walls (bubbles with two insides) and ultra-extreme walls (bubbles of false vacuum decay) are discussed. Their respective energy densities are higher and lower than that of the corresponding extreme (supersymmetric), planar domain wall. These singularity free space-times exhibit non-trivial causal structure analogous to certain non-extreme black holes. We focus on anti-de~Sitter--Minkowski walls and comment on Minkowski--Minkowski walls with trivial extreme limit, as well as walls adjacent to de~Sitter space-times with no extreme limit.
Minkowski Space is the simplest four-dimensional Lorentzian Manifold, being topologically trivial and globally flat, and hence the simplest model of spacetime--from a General-Relativistic point of view. But this does not mean that it is altogether structurally trivial. In fact, it has a very rich structure, parts of which will be spelled out in detail in this contribution. This will contain elementary aspects of affine spaces, various paths to the Poincare group, the lattices of causally and chronologically complete regions, and last but not least, the Noether-Herglotz theorem.
The two-point Wightman function of the free photon field defined in a gauge-invariant manner is known to be equivalent to the field-strength two-point function in any spacetime that is topologically trivial. We show that the gauge-invariant graviton two-point function defined in a similar manner is equivalent to the Weyl-tensor two-point function in Minkowski space and in the Poincare patch of de Sitter space. This implies that in the Poincare patch of de Sitter space the gauge-invariant graviton two-point function decays like (distance)^(-4) as a function of coordinate distance for spacelike …
For decades, a lot of work has been devoted to the problem of constructing a non-trivial quantum field theory in four-dimensional space time. This letter addresses the attempts to construct an algebraic quantum field theory in the framework of non-standard theories like hyperfunction or ultra-hyperfunction quantum field theory. For this purpose model theories of formally interacting neutral scalar fields are constructed and some of their characteristic properties like two-point functions are discussed. The formal self-couplings are obtained from local normally-ordered analytic redefinitions of…
We study exact tunneling solutions in scalar field theory for potential barriers composed of linear or quadratic patches. We analytically continue our solutions to imaginary Euclidean radius in order to study the profile of the scalar field inside the growing bubble. We find that generally there is a non-trivial profile of the scalar field, generating a stress-energy tensor, that depending on the form of the potential, can be a candidate for dark energy.
A model of the self-interacting charged massive spin-two field is constructed. We investigate several properties of the model and find that the trivial vacuum is only allowed due to the internal symmetry. This suggests that the Higgs mechanism might not be induced by the model of the massive spin-two field with the ghost-free potential.
We show how cosmological correlation functions of massless fields can be rewritten in terms of Minkowski correlation functions, by extracting symmetry-breaking operators from the cosmological correlators. This technique simplifies some cosmological calculations. Also, known properties of Minkowski correlation functions can be translated to non-trivial properties of cosmological correlations. To illustrate this idea, inflation to Minkowski and matter bounce to Minkowski relations are presented for the interactions of general single field inflation. And a Minkowski recursion relation is translat…
We construct a non-commutative kappa-Minkowski deformation of U(1) gauge theory, following a general approach, recently proposed in JHEP 2008 (2020) 041. We obtain an exact (all orders in the non-commutativity parameter) expression for both the deformed gauge transformations and the deformed field strength, which is covariant under these transformations. The corresponding Yang-Mills Lagrangian is gauge covariant and reproduces the Maxwell Lagrangian in the commutative limit. Gauge invariance of the action functional requires a non-trivial integration measure which, in the commutative limit, do…
Thermal fluctuations for a massive scalar field in the Rindler wedge are obtained by applying the point-splitting procedure to the zero temperature Feynman propagator in a conical spacetime. Renormalization is implemented by removing the zero temperature contribution. It is shown that for a field of non vanishing mass the thermal fluctuations, when expressed in terms of the local temperature, do not have Minkowski form. As a by product, Minkowski vacuum fluctuations seen by an uniformly accelerated observer are determined and confronted with the literature.
We show that strictly stationary spacetimes cannot have non-trivial configurations of form fields/complex scalar fields and then the spacetime should be exactly Minkowski or anti-deSitter spacetimes depending on the presence of negative cosmological constant. That is, self-gravitating complex scalar fields and form fields cannot exist.
We show how to generate non-trivial solutions to the conformally invariant, relativistic fluid dynamic equations by appealing to the Weyl covariance of the stress tensor. We use this technique to show that a recently studied solution of the relativistic conformally invariant Navier-Stokes equations in four-dimensional Minkowski space can be recast as a static flow in three-dimensional de Sitter space times a line. The simplicity of the de Sitter form of the flow enables us to consider several generalizations of it, including flows in other spacetime dimensions, second order viscous corrections…
Minkowski space can be sliced, outside the lightcone, in terms of Euclidean Anti-de Sitter and Lorentzian de Sitter slices. In this paper we investigate what happens when we apply holography to each slice separately. This yields a dual description living on two spheres, which can be interpreted as the boundary of the light cone. The infinite number of slices gives rise to a continuum family of operators on the two spheres for each separate bulk field. For a free field we explain how the Green's function and (trivial) S-matrix in Minkowski space can be reconstructed in terms of two-point functi…
New classes of exact M(em)brane solutions in M+2 dimensional Minkowski space are presented (some describing non-trivial topology changes, while others explicitly avoid finite-time singularity formation)
We consider the static charged black hole bomb system, originally designed for a (uncharged) rotating superradiant system by Press and Teukolsky. A charged scalar field confined in a Minkowski cavity with a Maxwell gauge field has a quantized spectrum of normal modes that can fit inside the box. Back-reacting non-linearly these normal modes, we find the hairy solitons, a.k.a boson stars (depending on the chosen $U(1)$ gauge), of the theory. The scalar condensate is totally confined inside the box and, outside it, we have the Reissner-Nordström solution. The Israel junction conditions at the bo…
Within the setting of a recently proposed model of quantum fields on noncommutative Minkowski spacetime, the consequences of the consistent application of the proper, untwisted Poincare group as the symmetry group are investigated. The emergent model contains an infinite family of fields which are labelled by different noncommutativity parameters, and related to each other by Lorentz transformations. The relative localization properties of these fields are investigated, and it is shown that to each field one can assign a wedge-shaped localization region of Minkowski space. This assignment is c…
We consider the approach to gravity in which four-dimensional curved spacetime is represented by a surface in a flat Minkowski space of higher dimension. After a short overview of the ideas and results of such an approach we concentrate on the study of the so-called splitting gravity, a form of this description in which constant value surface of a set of scalar fields in the ambient flat space-time defines the embedded surface. We construct a form of action which is invariant w.r.t. all symmetries of this theory. We construct the canonical formalism for splitting gravity. The resulting theory …
Recent Planck results motivated us to use non-Bunch-Davies vacuum. In this paper, we use the excited-de Sitter mode as non-linear initial states during inflation to calculate the corrected spectra of the initial fluctuations of the scalar field. First, we consider the field in de Sitter space-time as background field and for the non-Bunch-Davies mode, we use the perturbation theory to the second order approximation. Also, unlike conventional renormalization method, we offer de Sitter space-time as the background instead Minkowski space-time. This approach preserve the symmetry of curved space-…
We present an exact plane wave solution of the most general shift-symmetric Horndeski (generalized Galileon) theory. The solution consists of the scalar part, and the gravitational part with two polarization modes. The former is due to the presence of the non-trivial Galileon scalar field, and it is parametrized by an arbitrary function of the light-cone coordinate. For a trivial scalar field configuration the solution is equivalent to the plane gravitational wave in General Relativity. When the metric is Minkowski, we reproduce known results for the plane waves of k-essence and a soliton-like…
The spectrum of the Hamiltonian of the double compactified D=11 supermembrane with non-trivial central charge or equivalently the non-commutative symplectic super Maxwell theory is analyzed. In distinction to what occurs for the D=11 supermembrane in Minkowski target space where the bosonic potential presents string-like spikes which render the spectrum of the supersymmetric model continuous, we prove that the potential of the bosonic compactified membrane with non-trivial central charge is strictly positive definite and becomes infinity in all directions when the norm of the configuration spa…
We study a sixth order derivative scalar field model in Minkowski spacetime as a toy model of higher-derivative critical gravity theories. This model is consistently quantized when using the Becchi-Rouet-Stora-Tyutin (BRST) quantization scheme even though it does not show gauge symmetry manifestly. Imposing a BRST quartet generated by two scalars and ghosts, there remains a non-trivial subspace with positive norm. This might be interpreted as a Minkowskian dual version of the unitary truncation in the logarithmic conformal field theory.
We study the propagation of quantum fields on $κ$-Minkowsi spacetime. Starting from the non-commutative partition function for a free field written in momentum space we derive the Feynman propagator and analyze the non-trivial singularity structure determined by the group manifold geometry of momentum space. The additional contributions due to such singularity structure result in a deformed field propagation which can be alternatively described in terms of an ordinary field propagation determined by a source with a blurred spacetime profile. We show that the $κ$-deformed Feynman propagator can…
We conclude the rigorous analysis of a previous paper concerning the relation between the (Euclidean) point-splitting approach and the local $ζ$-function procedure to renormalize physical quantities at one-loop in (Euclidean) QFT in curved spacetime. The stress tensor is now considered in general $D$-dimensional closed manifolds for positive scalar operators $-Δ+ V(x)$. Results obtained in previous works (in the case D=4 and $V(x) =ξR(x) + m^2$) are rigorously proven and generalized. It is also proven that, in static Euclidean manifolds, the method is compatible with Lorentzian-time analytic c…
Emission of hard microscopic string (graviton) by an excited macroscopic string may be viewed as a model of branching of a $(1+1)$-dimensional baby universe off large parent one. We show that, apart from a trivial factor, the total emission rate is not suppressed by the size of the macroscopic string. This implies unsuppressed loss of quantum coherence in $(1+1)$-dimensional parent universe.
We consider $2d$ sigma models with a $D=2+N$ - dimensional Minkowski signature target space metric having a covariantly constant null Killing vector. These models are UV finite. The $2+N$-dimensional target space metric can be explicitly determined for a class of supersymmetric sigma models with $N$-dimensional `transverse' part of the target space being homogeneous Kähler. The corresponding `transverse' sub-theory is an $n=2$ supersymmetric sigma model with the exact $\gb$-function coinciding with its one-loop expression. For example, the finite $D=4$ model has $O(3)$ supersymmetric sigma mod…
Schwinger pair production is analyzed in a BPST instanton background and in its SL$(2,\mathbb{C})$ complex extension for complex scalar particles. A non-Abelian extension of the worldline instanton method is utilized, wherein Wong's equations in a coherent state picture adopted for SL$(2,\mathbb{C})$ are solved in Euclidean spacetime. While pair production is not predicted in the BPST instanton, a complex extension of the BPST instanton, existing as parallel fields in Minkowski spacetime, is shown to decay via the Schwinger effect.
We show that a non-trivial topological effect breaks the conformal invariance of pure Yang-Mills theory. Thus it is possible that classic particle-like solutions exists in pure non-Abelian Yang-Mills theory. We find a static, non-singular solution in source-free SU(2) Yang-Mills theory in four-dimensional Minkowski space. This solution is a stable soliton characterized by non-trivial topology and imaginary $A_0^a$, i.e., $A_0^aA_0^a<0$. It yields hermitian Hamilton, and finite, positive energy.
Conformal invariance for bosonic strings in time-dependent backgrounds of graviton, dilaton and Kalb-Ramond field is obtained by imposing Weyl-beta functions to be homogeneous in time, to all orders in $α^{'}$. This construction is possible in any target space dimension, as a result of the non-trivial background configurations. The electromagnetic effects of the antisymmetric tensor field, when coupled to an Abelian (electromagnetic) gauge field, are discussed in the framework of a four-dimensional Minkowski Universe, for concreteness. Non-trivial optical activity is demonstrated, which consti…
We show that for a SU(N) Yang-Mills theory the classical background-quantum splitting is non-trivially deformed at the quantum level by a canonical transformation with respect to the Batalin-Vilkovisky bracket associated with the Slavnov-Taylor identity of the theory. This canonical transformation acts on all the fields (including the ghosts) and antifields; it uniquely fixes the dependence on the background field of all the one-particle irreducible Green's functions of the theory at hand. The approach is valid both at the perturbative and non-perturbative level, being based solely on symmetry…
We prove a new type of finite time blow-up for a class of semilinear wave equations on extremal black holes. The initial data can be taken to be arbitrarily close to the trivial data. The first singularity occurs along the (degenerate) future event horizon. No analogue of this instability occurs for subextremal black holes or the Minkowski spacetime.
We consider the most general form for eleven dimensional supersymmetry compatible with on-shell superfields. This allows for the introduction of a conformal Spin(1,10) connection. In eleven dimensional Minkowski space this modification is trivial and can be removed by a field redefinition, however, upon compactification on S^1 it is possible to introduce a non-trivial `Wilson line'. The resulting ten dimensional supergravity has massive 1-form and 3-form potentials and a cosmological constant. This theory does not possess a supersymmetric eightbrane soliton but it does admit a supersymmetric n…
We study Wilson loops in N=4 SYM theory which are non-constant in the scalar (S5) directions and open string solutions associated with them in the context of AdS/CFT correspondence. An interplay between Minkowskian and Euclidean pictures turns out to be non-trivial for time-dependent Wilson loops. We find that in the S5-rotating case there appears to be no direct open-string duals for the Minkowskian Wilson loops, and their expectation values should be obtained by analytic continuation from the Euclidean-space results. In the Euclidean case, we determine the dependence of the ``quark - anti-qu…
