Bosonic String Research Articles

Gravitational and dilatonic radiations from the parallel dressed-dynamical unstable D[formula omitted]-branes

In the context of the bosonic string theory, we shall extract the general radiation amplitude of a massless closed string from the interaction of two parallel unstable Dp-branes. The branes are non-stationary and have been dressed by background fields. The foregoing amplitude will be rewritten for the massless state radiation from the branes with the large distance. Besides, we shall study the gravitational and dilatonic radiations from this configuration.

The exact [formula omitted] symmetry of string theory

By using on-shell recursion relation of string scattering amplitudes (SSA), we show that all n-point SSA of the open bosonic string theory can be expressed in terms of the Lauricella functions. This result extends the previous exact SL(K+3,C) symmetry of the 4-point Lauricella SSA (LSSA) of three tachyons and one arbitrary string states to the whole tree-level open bosonic string theory. Moreover, we present three applications of the SL(K+3,C) symmetry on the SSA. They are the solvability of all n-point SSA in terms of four-tachyon amplitudes, the existence of iteration relations among residues of a given SSA so as to soften its hard scattering behavior and finally the re-derivation of infinite linear relations among hard SSA [12].

Derived brackets in bosonic string sigma-model

We study the worldsheet theory of bosonic string from the point of view of the BV formalism. We explicitly describe the derived Poisson structure which arises when we expand the Master Action near a Lagrangian submanifold. The resulting higher Poisson brackets are all degenerate and essentially constant along their symplectic leaves. Deformations of the worldsheet complex structures define a family of Lagrangian submanifolds, parametrized by Beltrami differential. The worldsheet action depends nonlinearly on the Beltrami differential, but the structure of nonlinearity is governed by the BV Master Equation. This helps to clarify the mechanism of holomorphic factorization of string amplitudes.

$\mathrm{T}\overline{\mathrm{T}}$-deformed 1d Bose gas

\mathrm{T}\bar{\mathrm{T}}TT‾ deformation was originally proposed as an irrelevant solvable deformation for 2d relativistic quantum field theories (QFTs). The same family of deformations can also be defined for integrable quantum spin chains which was first studied in the context of integrability in AdS/CFT. In this paper, we construct such deformations for yet another type of models, which describe a collection of particles moving in 1d and interacting in an integrable manner. The prototype of such models is the Lieb-Liniger model. This shows that such deformations can be defined for a very wide range of systems. We study the finite volume spectrum and thermodynamics of the \mathrm{T}\overline{\mathrm{T}}TT¯-deformed Lieb-Liniger model. We find that for one sign of the deformation parameter (\lambda<0)(λ<0), the deformed spectrum becomes complex when the volume of the system is smaller than certain critical value, signifying the break down of UV physics. For the other sign (\lambda>0)(λ>0), there exists an upper bound for the temperature, similar to the Hagedorn behavior of the \mathrm{T}\overline{\mathrm{T}}TT¯ deformed QFTs. Both behaviors can be attributed to the fact that \mathrm{T}\overline{\mathrm{T}}TT¯ deformation changes the size the particles. We show that for \lambda>0λ>0, the deformation increases the spaces between particles which effectively increases the volume of the system. For \lambda<0λ<0, \mathrm{T}\overline{\mathrm{T}}TT¯ deformation fattens point particles to finite size hard rods. This is similar to the observation that the action of \mathrm{T}\overline{\mathrm{T}}TT¯-deformed free boson is the Nambu-Goto action, which describes bosonic strings — also an extended object with finite size.

Different kind of four-dimensional brane for string theory

We present a generalization of the string's Polyakov action that describes a conformally invariant four-dimensional brane. The new extended object is very different from the traditional D-branes of string theory, but, nevertheless, shares some structural similarities with the string, especially when it comes to the low-energy limit of small tension. We introduce a rather rich structure of tensors that can play a role at low energies. In analogy with the bosonic string, we initiate the quantization of the new brane discussing the extent in which it produces a critical dimension of spacetime and Einstein's equations coupled to a scalar dilaton under some approximations.

Resolving naked singularities in alpha ^{prime }-corrected string theory

Low energy effective action of bosonic string theory possesses a kind of singular static solution which can be interpreted as a naked singularity. Based on the Hohm–Zwiebach action, the naked singularities could be smoothed out by introducing the complete alpha ^{prime } corrections of string theory. In this paper, we present two sets of non-singular solutions, which are also regular everywhere in the Einstein frame. In the perturbative region alpha ^{prime }rightarrow 0, the solutions reduce to the perturbative results. Our result provides extra evidence for weak cosmic censorship conjecture (WCCC) from a viewpoint of string theory.

Note about string theory with deformed dispersion relations

The goal of this short paper is to find Lagrangian for bosonic string with deformed dispersion relation proposed by J. Magueijo and L. Smolin in 2004. We also show that in the preferred case \(f=g\) this Lagrangian reduces into Nambu-Gotto form of relativistic string without modification of the dispersion relation.

Background independence of effective actions at critical dimension

Recently, by explicit calculations at orders $\alpha',\alpha'^2,\alpha'^3$, it has been observed that the effective action of string theory at the critical dimension is independent of the background for the closed spacetime manifolds. In this paper we speculate that for the open spacetime manifolds, the effective action is even independent of the character of the boundary, \ie the boundary couplings for timelike and spacelike boundaries are the same. We support this proposal by calculating the boundary couplings in the bosonic string theory at order $\alpha'$ for the spacelike boundary and show that they are the same as the couplings for the timelike boundary that have been recently found.

Geometric quantization: Particles, fields and strings

These notes present an introduction to the method of geometric quantization. We discuss the main theorems in a style suitable for a theoretical physicist with an eye towards the physical motivation and the interpretation of the geometric construction as providing a solution to Dirac’s axioms of quantization. We provide in detail the examples of free relativistic particles, their corresponding quantum fields, and the bosonic string using formalism of double field theory. This paper is based on lectures written by Gabriel Cardoso.

Scattering amplitudes of Kaluza-Klein strings and extended massive double-copy

We study the scattering amplitudes of massive Kaluza-Klein (KK) states of open and closed bosonic strings under toroidal compactification. We analyze the structure of vertex operators for the KK strings and derive an extended massive KLT-like relation which connects the N-point KK closed-string amplitude to the products of two KK open-string amplitudes at tree level. Taking the low energy field-theory limit of vanishing Regge slope, we derive double-copy construction formula of the N-point massive KK graviton amplitude from the sum of proper products of the corresponding KK gauge boson amplitudes. Then, using the string-based massive double-copy formula, we derive the exact tree-level four-point KK gauge boson amplitudes and KK graviton amplitudes, which fully agree with those given by the KK field-theory calculations. With these, we give an explicit prescription on constructing the exact four-point KK graviton amplitudes from the sum of proper products of the corresponding color-ordered KK gauge boson amplitudes. We further analyze the string-based double-copy construction of five-point and six-point scattering amplitudes of massive KK gauge bosons and KK gravitons.

Torsional string Newton-Cartan geometry for non-relativistic strings

We revisit the formulation of non-relativistic (NR) string theory and its target space geometry. We obtain a new formulation in which the geometry contains a two-form field that couples to the tension current and that transforms under string Galilei boosts. This parallels the Newton-Cartan one-form that couples to the mass current of a non-relativistic point particle. We show how this formulation of the NR string arises both from an infinite speed of light limit and a null reduction of the relativistic closed bosonic string. In both cases, the two-form originates from a combination of metric quantities and the Kalb-Ramond field. The target space geometry of the NR string is seen to arise from the gauging of a new algebra that is obtained by an İnönü-Wigner contraction of the Poincaré algebra extended by the symmetries of the Kalb-Ramond field. In this new formulation, there are no superfluous target space fields that can be removed by fixing a Stückelberg symmetry. Classically, there are no foliation/torsion constraints imposed on the target space geometry.

Duality invariant string beta functions at two loops

We compute, for cosmological backgrounds, the O(d, d; ℝ) invariant beta functions for the sigma model of the bosonic string at two loops. This yields an independent first-principle derivation of the order α′ corrections to the cosmological target-space equations. To this end we revisit the quantum consistency of Tseytlin’s duality invariant formulation of the worldsheet theory. While we confirm the absence of gravitational (and hence Lorentz) anomalies, our results show that the minimal subtraction scheme is not applicable, implying significant technical complications at higher loops. To circumvent these we then change gears and use the Polyakov action for cosmological backgrounds, applying a suitable perturbation scheme that, although not O(d, d; ℝ) invariant, allows one to efficiently determine the O(d, d; ℝ) invariant beta functions.

Nilpotent Symmetries of a Model of 2D Diffeomorphism Invariant Theory: BRST Approach

Within the framework of the Becchi-Rouet-Stora-Tyutin (BRST) formalism, we discuss the full set of proper BRST and anti-BRST transformations for a 2D diffeomorphism invariant theory which is described by the Lagrangian density of a standard bosonic string. The above (anti-)BRST transformations are off-shell nilpotent and absolutely anticommuting. The latter property is valid on a submanifold of the space of quantum fields where the 2D version of the universal (anti-)BRST invariant Curci-Ferrari (CF) type of restrictions is satisfied. We derive the precise forms of the BRST and anti-BRST invariant Lagrangian densities as well as the exact expressions for the conserved (anti-)BRST and ghost charges. The lucid derivation of the proper anti-BRST symmetry transformations and the emergence of the CF-type restrictions are completely novel results for our present bosonic string which has already been discussed earlier in literature where only the BRST symmetry transformations have been pointed out. We briefly mention the derivation of the CF-type restrictions from the modified version of the Bonora-Tonin superfield approach, too.

Radiation of closed strings between the parallel dynamical-dressed unstable Dp-branes

We introduce a boundary state which is corresponding to a Dp-brane with tangential dynamics in the presence of the Kalb-Ramond field, a tachyonic field and a U(1) gauge potential in a special gauge. From the interaction of such branes radiation amplitude of a general massless closed string will be computed. The effects of the large distances of the branes on this radiation will be studied. In the large distances of the branes, the possibility of axion radiation will be investigated. Our calculations will be in the context of the bosonic string theory.

Nonrelativistic Expansion of Closed Bosonic Strings.

We develop a novel approach to nonrelativistic closed bosonic string theory that is based on a string 1/c^{2} expansion of the relativistic string, where c is the speed of light. This approach has the benefit that one does not need to take a limit of a string in a near-critical Kalb-Ramond background. The 1/c^{2}-expanded Polyakov action at next-to-leading order reproduces the known action of nonrelativistic string theory provided that the target space obeys an appropriate foliation constraint. We compute the spectrum in a flat target space, with one circle direction that is wound by the string, up to next-to-leading order and show that it reproduces the spectrum of the Gomis-Ooguri string.

General relativity from $p$-adic strings

For an arbitrary prime number $p$, we propose an action for bosonic $p$-adic strings in curved target spacetime, and show that the vacuum Einstein equations of the target are a consequence of worldsheet scaling symmetry of the quantum $p$-adic strings, similar to the ordinary bosonic strings case. It turns out that certain $p$-adic automorphic forms are the plane wave modes of the bosonic fields on $p$-adic strings, and that the regularized normalization of these modes on the $p$-adic worldsheet presents peculiar features which reduce part of the computations to familiar setups in quantum field theory, while also exhibiting some new features that make loop diagrams much simpler. Assuming a certain product relation, we also observe that the adelic spectrum of the bosonic string corresponds to the nontrivial zeros of the Riemann Zeta function.

Celestial OPEs and w1+\u221e algebra from worldsheet in string theory

Celestial operator product expansions (OPEs) arise from the collinear limit of scattering amplitudes and play a vital role in celestial holography. In this paper, we derive the celestial OPEs of massless fields in string theory from the worldsheet. By studying the worldsheet OPEs of vertex operators in worldsheet CFT and further examining their behaviors in the collinear limit, we find that new vertex operators for the massless fields in string theory are generated and become dominant in the collinear limit. Mellin transforming to the conformal basis yields exactly the celestial OPEs in celestial CFT. We also derive the celestial OPEs from the collinear factorization of string amplitudes and the results derived in these two different methods are in perfect agreement with each other. Our final formulae of celestial OPEs are applicable to general dimensions, corresponding to Einstein-Yang-Mills theory supplemented by some possible higher derivative interactions. Specializing to 4D, we reproduce all the celestial OPEs for gluon and graviton in the literature. We consider various string theories, including the open and closed bosonic string, as well as the closed superstring theory with mathcal{N} = 1 and mathcal{N} = 2 worldsheet supersymmetry. In the case of mathcal{N} = 2 string, we also derive all the overline{mathrm{SL}left(2,mathbb{R}right)} descendant contributions in the celestial OPE; the soft sector of such OPE just yields the w1+∞ algebra after rewriting in terms of chiral modes. Our stringy derivation of celestial OPEs thus initiates the first step towards the microscopic realization of celestial CFT dual to string theory in flat spacetime.

Spinning-off stringy electro-magnetic memories

We extend and generalise the string corrections to the EM memory to the Type I superstring including spin effects. Very much as in the simpler bosonic string context, the relevant corrections are non-perturbative in α′, slowly decaying (as 1/R) at large distances and modulated in retarded time u=t−R. For spin N states in the first Regge trajectory they entail a sequence of N derivatives wrt u on the ‘parent’ N=0 amplitude. We also briefly discuss how to include loop effects, that broaden and shift the string resonances, and how to modify our analysis for macroscopic semi-classical quasi-BPS coherent states, whose collisions may lead to detectable string memory signals in viable Type I models.

Higher-spin states of the superstring in an electromagnetic background

Constructing a consistent four-dimensional Lagrangian for charged massive higher-spin fields propagating in an electromagnetic background is an open problem. In 1989, Argyres and Nappi used bosonic open string field theory to construct a Lagrangian for charged massive spin-2 fields in a constant electromagnetic background. In this paper, we use the four-dimensional hybrid formalism for open superstring field theory to construct a supersymmetric Lagrangian for charged massive spin-2 and spin-3/2 fields in a constant electromagnetic background. The hybrid formalism has the advantage over the RNS formalism of manifest mathcal{N} = 1 d=4 spacetime supersymmetry so that the spin-2 and spin-3/2 fields are combined into a single superfield and there is no need for picture-changing or spin fields.

Green-Schwarz and pure spinor formulations of chiral strings

Bosonic and RNS chiral strings have been defined from a singular gauge fixing of the respective Polyakov and spinning string actions, enforcing, among other things, the finite nature of their physical spectra. Except for the heterotic case, the tensionless limits of such chiral models have been shown to describe the same field theories predicted by their ambitwistor analogues. In this paper, we study the Green-Schwarz formulation for Type II and heterotic superstrings in a singular gauge. After performing a light-cone gauge analysis, their physical spectra are shown to match those of RNS chiral strings, and their respective tensionless limits are found to describe the same field theories predicted by RNS ambitwistor strings. Their pure spinor counterparts are then introduced by making use of the Oda-Tonin method. In doing so, symmetries hidden in the pure spinor ambitwistor string action become manifest, proposals motivating the sectorized pure spinor BRST charges find simple grounds, and integrated vertex operators emerge naturally.