Solutions In Field Theory Research Articles

Stability of gravitating charged-scalar solitons in a cavity

We present new regular solutions of Einstein-charged scalar field theory in a cavity. The system is enclosed inside a reflecting mirror-like boundary, on which the scalar field vanishes. The mirror is placed at the zero of the scalar field closest to the origin, and inside this boundary our solutions are regular. We study the stability of these solitons under linear, spherically symmetric perturbations of the metric, scalar and electromagnetic fields. If the radius of the mirror is sufficiently large, we present numerical evidence for the stability of the solitons. For small mirror radius, some of the solitons are unstable. We discuss the physical interpretation of this instability.

BV analysis of tachyon fluctuation around multi-brane solutions in cubic string field theory

We study whether the tachyon mode exists as a physical fluctuation on the 2-brane solution and on the tachyon vacuum solution in cubic open string field theory. Our analysis is based on the Batalin-Vilkovisky formalism. We first construct a set of six string states which corresponds to the set of fields and anti-fields containing the tachyon field. Whether the tachyon field can exist as a physical fluctuation is determined by the 6x6 matrix defining the anti-bracket in the present sector. If the matrix is degenerate/non-degenerate, the tachyon field is physical/unphysical. Calculations for the pure-gauge type solutions in the framework of the KBc algebra and using the Ke-regularization lead to the expected results. Namely, the matrix for the anti-bracket is degenerate/non-degenerate in the case of the 2-brane/tachyon-vacuum solution. Our analysis is not complete, in particular, in that we have not identified the four-fold degeneracy of tachyon fluctuation on the 2-brane solution, and moreover that the present six states do not satisfy the hermiticity condition.

Dx-Schemes and Jets in Conformal Gravity Using Integral Transforms

A scheme is a scheme equipped with a flat connection over a smooth scheme on a base field. The flat connection equipment is a characterization of this scheme to construct through isomorphisms between commutative algebras and formal moduli problems the conformal images of the space-time that are solutions in conformal field theory. If are considered the schemes and their particular tools, the jets, these determine conformal blocks of space-time pieces that are invariant under conformal transformations. These conformal block of space-time pieces determine a homogeneous degree factor that characterizes the solutions in a complex Riemannian model of the space-time of the field equations to certain tensors of the Weyl curvature. Finally, is demonstrated that the algebra belonging to the schemes to the mentioned formal moduli problem is the image under a generalized Penrose transform that in the conformal context of many pieces of the space-time, has a structure as objects in commutative rings of CAlgk each one.

Solutions in bosonic string field theory and higher spin algebras in AdS

We find a class of analytic solutions in open bosonic string field theory, parametrized by the chiral copy of higher spin algebra in $AdS_3$. The solutions are expressed in terms of the generating function for the products of Bell polynomials in derivatives of bosonic space-time coordinates $X^m(z)$ of the open string, which form is determined in this work. The products of these polynomials form a natural operator algebra realizations of $W_\infty$ (area-preserving diffeomorphisms), enveloping algebra of SU(2) and higher spin algebra in $AdS_3$. The class of SFT solutions found can, in turn, be interpreted as the "enveloping of enveloping", or the enveloping of $AdS_3$ higher spin algebra. We also discuss the extensions of this class of solutions to superstring theory and their relations to higher spin algebras in higher space-time dimensions.

Solutions in Exceptional Field Theory

Exceptional Field Theory employs an extended spacetime to make supergravity fully covariant under the U‐duality groups of M‐theory. This allows for the wave and monopole solutions to be combined into a single solution which obeys a twisted self‐duality relation. All fundamental, solitonic and Dirichlet branes of ten‐ and eleven‐dimensonal supergravity may be extracted from this single solution in Exceptional Field Theory.

Dual localized objects from m-branes over

We consider a few ansatzs for the four and seven forms of 11-dimensional (11D) supergravity over while trying to keep the geometry unchanged. From the 4-form equations, we arrive at some massless scalars and pseudoscalars in the bulk of Euclidean that match with some boundary operators. Indeed, the main objects are instantons and domain walls as the fully and partially localized objects in the external space, respectively. The latter comes from an (anti)M5-brane wrapping partly around three internal directions similar to the fuzzy solutions. Except for the first solutions of adding some anti-M2-branes (M2-branes) to the original M2-branes, the objects backreact on the geometry although (break all supersymmetries and destabilize the vacua). The dual 3-dimensional field theory solutions are obtained by the skew-whiffing and for the scalars and pseudoscalars respectively, while the gauge fields are used mainly for the cases where the R-symmetry and supersymmetry are enhanced as and respectively, and also for pseudoscalars. Further, for the pseudoscalars we propose a special boundary deformation, with a fermion field, that is equivalent to a multi-trace deformation already studied for the bulk conformally coupled pseudoscalar.

Nonlinear gauge invariance and WZW-like action for NS-NS superstring field theory

We complete the construction of a gauge-invariant action for NS-NS superstring field theory in the large Hilbert space begun in arXiv:1305.3893 by giving a closed-form expression for the action and nonlinear gauge transformations. The action has the WZW-like form and vertices are given by a pure-gauge solution of heterotic string field theory in the small Hilbert space.

Strings, branes and the self-dual solutions of Exceptional Field Theory

It has been shown that membranes and fivebranes are wave-like or monopole-like solutions in some higher dimensional theory. Here the picture is completed by combining the wave and monopole solutions into a single solution of Exceptional Field Theory. This solution solves the twisted self-duality constraint. The 1/2 BPS brane spectrum, consisting of fundamental, solitonic and Dirichlet branes and their bound states, in ten- and eleven-dimensional supergravity may all be extracted from this single solution of Exceptional Field Theory. The solution’s properties such as its asymptotic behavior at the core and at infinity are investigated.

Renormalization schemes for SFT solutions

In this paper, we examine the space of renormalization schemes compatible with the Kiermaier and Okawa (1) framework for constructing Open String Field Theory solutions based on marginal operators with singular self-OPEs. We show that, due to freedom in dening the renormalization scheme which tames these singular OPEs, the solutions obtained from the KO framework are not necessarily unique. We identify a multidimensional space of SFT solutions corresponding to a single given marginal operator.

Comments on Takahashi-Tanimoto’s scalar solution

We study the identity-based solution of Witten's cubic bosonic open string field theory constructed by Takahashi and Tanimoto, which is claimed to describe the tachyon vacuum. We argue that the observables of the solution coincide with those of the tachyon vacuum using the method proposed by Kishimoto and Takahashi. We also discuss how to treat the kinetic term of the string field theory expanded around it.

Scale setting for self-consistent backgrounds

The quest for finding self-consistent background solutions in quantum field theory is closely related to the way one decides to set the renormalization scale $k$. This freedom in the choice of the scale setting can lead to ambiguities and conceptual inconsistencies such as the nonconservation of the stress-energy tensor. In this paper a setting for the ``scale field'' is proposed at the level of effective action, which avoids such inconsistencies by construction. The mechanism and its potential is exemplified for scalar ${\ensuremath{\phi}}^{4}$ theory and for Einstein-Hilbert-Maxwell theory.

Stationary and uniformly accelerated states in nonlinear quantum mechanics

We consider two kinds of solutions of a recently proposed field theory leading to a nonlinear Schr\odinger equation exhibiting solitonlike solutions of the power-law form ${e}_{q}^{i(kx\ensuremath{-}wt)}$, involving the $q$ exponential function naturally arising within nonextensive thermostatistics [${e}_{q}^{z}\ensuremath{\equiv}{[1+(1\ensuremath{-}q)z]}^{1/(1\ensuremath{-}q)}$, with ${e}_{1}^{z}={e}^{z}$]. These fundamental solutions behave like free particles, satisfying $p=\ensuremath{\hbar}k$, $E=\ensuremath{\hbar}\ensuremath{\omega}$, and $E={p}^{2}/2m$ $(1\ensuremath{\le}ql2)$. Here we introduce two additional types of exact, analytical solutions of the aforementioned field theory. As a first step we extend the theory to situations involving a potential energy term, thus going beyond the previous treatment concerning solely the free-particle dynamics. Then we consider both bound, stationary states associated with a confining potential and also time-evolving states corresponding to a linear potential function. These types of solutions might be relevant for physical applications of the present nonlinear generalized Schr\odinger equation. In particular, the stationary solution obtained shows an increase in the probability for finding the particle localized around a certain position of the well as one increases $q$ in the interval $1\ensuremath{\le}ql2$, which should be appropriate for physical systems where one finds a low-energy particle localized inside a confining potential.

New analytic solutions in string field theory: Towards a collective higher spin vacuum

We construct analytic solutions in cubic open superstring field theory at higher superconformal ghost numbers.The solutions are the pure ghost ones and are given by combinations of Bell polynomials of bosonized superconformal ghost fields multiplied by exponents of the bosonized ghosts. Based on the structure of the solutions, we conjecture them to describe the ghost part of collective vacuum for higher spin modes in open string theory.

A New Tool in Nuclear Physics: Nuclear Lattice Simulations

The nuclear many-body problem continues to be one of the most interesting and demanding challenges in contemporary physics. With the advent of FAIR, FRIB, and the many existing radioactive ion beam facilities, a detailed and accurate theoretical understanding of nuclear structure and reactions is mandatory. A major breakthrough in nuclear theory was initiated through the work of Steven Weinberg [1], who made the first steps for an effective field theory (EFT) solution of the nuclear force problem. In this approach, two- and multi-nucleon forces as well as the response to external electromagnetic and weak probes can be calculated systematically, precisely, and consistently. In addition, the so important issue of assigning theoretical errors can be dealt with naturally. The very hot topic of the quest for three-nucleon forces was already addressed in this journal [2], which also contained a short introduction into the framework of chiral nuclear EFT. In this scheme, the nuclear forces are given in terms of one-, two-, … pion exchanges and smeared local multi-nucleon operators, that parameterize the short-distance behavior of the nuclear forces. These operators come with unknown coupling constants, the so-called low-energy constants (LECs) that must be determined from a fit to nucleon-nucleon scattering and a few three-body data. For systems up to four nucleons, these forces have been tested in extensive detail and scrutinized. One of the present research foci is the calculation and investigation of higher order corrections to the three-nucleon forces as well as the construction of electroweak current operators. For reviews on the method and many results see Refs. [3, 4].

String field theory solution for any open string background

We present an exact solution of open bosonic string field theory which can be used to describe any time-independent open string background. The solution generalizes an earlier construction of Kiermaier, Okawa, and Soler, and assumes the existence of boundary condition changing operators with nonsingular OPEs and vanishing conformal dimension. Our main observation is that boundary condition changing operators of this kind can describe nearly any open string background provided the background shift is accompanied by a timelike Wilson line of sufficient strength. As an application we analyze the tachyon lump describing the formation of a D$(p-1)$-brane in the string field theory of a D$p$-brane, for generic compactification radius. This not only provides a proof of Sen's second conjecture, but also gives explicit examples of higher energy solutions, confirming analytically that string field theory can "reverse" the direction of the worldsheet RG flow. We also find multiple D-brane solutions, demonstrating that string field theory can add Chan-Paton factors and change the rank of the gauge group. Finally, we show how the solution provides a remarkably simple and nonperturbative proof of the background independence of open bosonic string field theory.

Double field theory inspired cosmology

Double field theory proposes a generalized spacetime actionpossessing manifest T-duality on the level of component fields. Wecalculate the cosmological solutions of double field theory withvanishing Kalb-Ramond field. It turns out that double field theoryprovides a more consistent way to construct cosmological solutionsthan the standard string cosmology. We construct solutions for vanishing and non-vanishing symmetry preserving dilaton potentials. The solutions assemblethe pre- and post-big bang evolutions in one single line element.Our results show a smooth evolution from an anisotropic early stage to an isotropic phase without any special initial conditions in contrast to previous models. In addition, we demonstrate that the contraction of the dual space automatically leads to both an inflation phase and a decelerated expansion of the ordinary space during different evolution stages.

Strings and branes are waves

We examine the equations of motion of double field theory and the duality manifest form of M-theory. We show the solutions of the equations of motion corresponding to null pp-waves correspond to strings or membranes from the usual spacetime perspective. A Goldstone mode analysis of the null wave solution in double field theory produces the equations of motion of the duality manifest string.

A simple solution for marginal deformations in open string field theory

We derive a new open string field theory solution for boundary marginal deformations generated by chiral currents with singular self-OPE. The solution is algebraically identical to the Kiermaier-Okawa-Soler solution and it is gauge equivalent to the TakahashiTanimoto identity-based solution. It is wedge-based and we can analytically evaluate the Ellwood invariant and the action, reproducing the expected results from BCFT. By studying the isomorphism between the states of the initial and final background a dual derivation of the Ellwood invariant is also obtained.

Giant monopoles as a dark matter candidate

The most prominent successes of weakly interacting massive particle (WIMP) models of dark matter are at comoving scales of megaparsecs. At kiloparsec scales they face challenges in explaining the density profiles, abundances and phase space distributions of satellite galaxies in our local group. An alternate dark matter candidate, the giant 't Hooft-Polyakov monopole, is proposed which may share the large distance successes of WIMPs while evading their short distance problems. These are classical field theory solutions of a dark sector including a nonabelian gauge field, an adjoint scalar field and fundamental fermions. In such models each halo consists of a single monopole characterized by a conserved integer charge.

Scalar field breathers on anti–de Sitter background

We study spatially localized, time-periodic solutions (breathers) of scalar field theories with various self-interacting potentials on Anti-de Sitter (AdS) spacetimes in $D$ dimensions. A detailed numerical study of spherically symmetric configurations in $D=3$ dimensions is carried out, revealing a rich and complex structure of the phase-space (bifurcations, resonances). Scalar breather solutions form one-parameter families parametrized by their amplitude, $\varepsilon$, while their frequency, $\omega=\omega(\varepsilon)$, is a function of the amplitude. The scalar breathers on AdS we find have a small amplitude limit, tending to the eigenfunctions of the linear Klein-Gordon operator on AdS. Importantly most of these breathers appear to be generically stable under time evolution.