Bosonic String Research Articles

Spacetime dilaton in AdS3 × X holography

Abstract We study the spectrum generating operators (DDF operators) for bosonic strings and superstrings in AdS3 × X with pure, generic NSNS flux. The dual CFT is conjectured to be a deformed symmetric orbifold of $$ {\mathbb{R}}_{\overset{\sim }{Q}}\times X $$ ℝ Q ~ × X , where $$ {\mathbb{R}}_{\overset{\sim }{Q}} $$ ℝ Q ~ denotes a linear dilaton theory with slope $$ \overset{\sim }{Q} $$ Q ~ . In this paper, we construct DDF operators corresponding to the spacetime linear dilaton field in the limit where the worldsheet theory becomes free. The DDF operator gives another evidence supporting the proposed dual CFT. Furthermore, the DDF operator is constructed purely from the AdS3 fields and thus, strongly implies the existence of $$ {\mathbb{R}}_{\overset{\sim }{Q}} $$ ℝ Q ~ for generic X that defines a consistent background.

K27 as a symmetry of closed bosonic strings and branes

<i>K</i>₂₇ as a symmetry of closed bosonic strings and branes

(Pseudo-)Synthetic BRST quantisation of the bosonic string and the higher quantum origin of dualities

In this article I am arguing in favour of the hypothesis that the origin of gauge and string dualities in general can be found in a higher-categorical interpretation of basic quantum mechanics. It is interesting to observe that the Galilei group has a non-trivial cohomology, while the Lorentz/Poincare group has trivial cohomology. When we constructed quantum mechanics, we noticed the non-trivial cohomology structure of the Galilei group and hence, we required for a proper quantisation procedure that would be compatible with the symmetry group of our theory, to go to a central extension of the Galilei group universal covering by co-cycle. This would be the Bargmann group. However, Nature didn’t choose this path. Instead in nature, the Galilei group is not realised, while the Lorentz group is. The fact that the Galilei group has topological obstructions leads to a central charge, the mass, and a superselection rule, required to implement the Galilei symmetry, that forbids transitions between states of different mass. The topological structure of the Lorentz group however lacks such an obstruction, and hence allows for transitions between states of different mass. The connectivity structure of the Lorentz group as opposed to that of the Galilei group can be interpreted in the sense of an ER=EPR duality for the topological space associated to group cohomology. In string theory we started with the Witt algebra, and due to similar quantisation issues, we employed the central extension by co-cycle to obtain the Virasoro algebra. This is a unique extension for orientation preserving diffeomorphisms on a circle, but there is no reason to believe that, at the high energy domain in physics where this would apply, we do not have a totally different structure altogether and the degrees of freedom present there would require something vastly more general and global.

Non-relativistic expansion of open strings and D-branes

We expand the relativistic open bosonic string in powers of 1/c2 where c is the speed of light. We perform this expansion to next-to-leading order in 1/c2 and relate our results to known descriptions of non-relativistic open strings obtained by taking limits. Just as for closed strings the non-relativistic expansion is well-defined if the open string winds a circle in the target space. This direction must satisfy Dirichlet boundary conditions. It is shown that the endpoints of the open string behave as Bargmann particles in the non-relativistic regime. These open strings end on nrDp-branes with p ≤ 24. When these nrDp-branes do not fluctuate they correspond to (p + 1)-dimensional Newton-Cartan submanifolds of the target space. When we include fluctuations and worldvolume gauge fields their dynamics is described by a non-relativistic version of the DBI action whose form we derive from symmetry considerations. The worldvolume gauge field and scalar field of a nrD24-brane make up the field content of Galilean electrodynamics (GED), and the effective theory on the nrD24-brane is precisely a non-linear version of GED. We generalise these results to actions for any nrDp-brane by demanding that they have the same target space gauge symmetries that the non-relativistic open and closed string actions have. Finally, we show that the nrDp-brane action is transverse T-duality covariant. Our results agree with the findings of Gomis, Yan and Yu in [1].

On universal splittings of tree-level particle and string scattering amplitudes

In this paper, we study the newly discovered universal splitting behavior for tree-level scattering amplitudes of particles and strings [1]: when a set of Mandelstam variables (and Lorentz products involving polarizations for gluons/gravitons) vanish, the n-point amplitude factorizes as the product of two lower-point currents with n+3 external legs in total. We refer to any such subspace of the kinematic space of n massless momenta as “2-split kinematics”, where the scattering potential for string amplitudes and the corresponding scattering equations for particle amplitudes nicely split into two parts. Based on these, we provide a systematic and detailed study of the splitting behavior for essentially all ingredients which appear as integrands for open- and closed-string amplitudes as well as Cachazo-He-Yuan (CHY) formulas, including Parke-Taylor factors, correlators in superstring and bosonic string theories, and CHY integrands for a variety of amplitudes of scalars, gluons and gravitons. These results then immediately lead to the splitting behavior of string and particle amplitudes in a wide range of theories, including bi-adjoint ϕ3 (with string extension known as Z and J integrals), non-linear sigma model, Dirac-Born-Infeld, the special Galileon, etc., as well as Yang-Mills and Einstein gravity (with bosonic and superstring extensions). Our results imply and extend some other factorization behavior of tree amplitudes considered recently, including smooth splittings [2] and factorizations near zeros [3], to all these theories. A special case of splitting also yields soft theorems for gluons/gravitons as well as analogous soft behavior for Goldstone particles near their Adler zeros.

T‐Duality of a Bosonic String in a Weakly Curved Space‐Time

AbstractIn this article, the T‐dualization of a 3D closed bosonic string, that is propagating in space‐time metric with an infinitesimal linear dependence on the coordinates xμ, is considered. Other fields, Kalb‐Ramond and dilaton fields are set to zero. Action with this configuration of fields is not invariant to translations. In order to find the T‐dual theory, a generalization of the Buscher procedure is employed, that can be applied to cases with coordinate dependent fields that do not possess translational isometry. Finally, by using transformation laws that connect coordinates of starting and T‐dual theories, authors will be able to examine the geometric structure of T‐dual theory.

Chaotic and thermal aspects in the highly excited string S-matrix

We compute tree level scattering amplitudes involving more than one highly excited states and tachyons in bosonic string theory. We use these amplitudes to understand the chaotic and thermal aspects of the excited string states lending support to the Susskind-Horowitz-Polchinski correspondence principle. The unaveraged amplitudes exhibit chaos in the resonance distribution as a function of the kinematic parameters, which can be described by random matrix theory. Upon coarse-graining, these amplitudes are shown to exponentiate, and capture various thermal features, including features of a stringy version of the eigenstate thermalization hypothesis as well as notions of typicality. Further, we compute the effective string form factor corresponding to the highly excited states, and argue for the random walk behaviour of the long strings.

Confining strings in three-dimensional gauge theories beyond the Nambu-Gotō approximation

We carry out a systematic study of the effective bosonic string describing confining flux tubes in SU(N) Yang-Mills theories in three spacetime dimensions. While their low-energy properties are known to be universal and are described well by the Nambu-Gotō action, a non-trivial dependence on the gauge group is encoded in a series of undetermined subleading corrections in an expansion around the limit of an arbitrarily long string. We quantify the first two of these corrections by means of high-precision Monte Carlo simulations of Polyakov-loop correlators in the lattice regularization. We compare the results of novel lattice simulations for theories with N = 3 and 6 color charges, and report an improved estimate for the N = 2 case, discussing the approach to the large-N limit. Our results are compatible with analytical bounds derived from the S-matrix bootstrap approach. In addition, we also present a new test of the Svetitsky-Yaffe conjecture for the SU(3) theory in three dimensions, finding that the lattice results for the Polyakov-loop correlation function are in excellent agreement with the predictions of the Svetitsky-Yaffe mapping, which are worked out quantitatively applying conformal perturbation theory to the three-state Potts model in two dimensions. The implications of these results are discussed.

Canonical lifts in multisymplectic De Donder–Weyl Hamiltonian field theories

We define canonical lifts of vector fields to the multisymplectic multimomentum bundles of De Donder–Weyl Hamiltonian (first-order) field theories and to the appropriate premultisymplectic embedded constraint submanifolds on which singular field theories are studied. These new canonical lifts are used to study the so-called natural Noether symmetries present in both regular and singular Hamiltonian field theories along with their associated conserved quantities obtained from Noether’s theorem. The Klein–Gordon field, the Polyakov bosonic string, and Einstein–Cartan gravity in 3+1 dimensions are analyzed in depth as applications of these concepts; as a peripheral result obtained in the analysis of the bosonic string, we provide a new geometrical interpretation of the well-known Virasoro constraint.

From the standard model to M-theory: The development of string theory

String theory is now the most competitive theory of quantum gravity, and it takes an important role in theoretical physics. In this article, we introduced why we need string theory and how string theory is formed. The importance of string theory is described through general relativity and the Standard Model of particle physics. String theory is originally discovered to describe strong interaction. While a better model for strong interaction was developed, string theory was found to be a candidate for a theory about quantum gravity. The first version of string theory is the bosonic string theory, which was constructed in 26-dimensional space and used to describe bosons. After supersymmetry was introduced, the dimensions were reduced to 10, and the theory is hence called the superstring theory. In the first superstring revolution, 5 different superstring theories were constructed and compactified on the 6-dimensional Calabi-Yau manifold. In the second superstring revolution, the idea of different dualities was introduced in string, as well as D-branes. Hence, it was found that the 5 different superstrings can be unified to get the 11-dimensional M-theory.

On the deep superstring spectrum

We propose a covariant method of constructing entire trajectories of physical states in superstring theory in the critical dimension. It is inspired by a recently developed covariant technology of excavating bosonic string trajectories, that is facilitated by the observation that the Virasoro constraints can be written as linear combinations of lowering operators of a bigger algebra, namely a symplectic algebra, which is Howe dual to the spacetime Lorentz algebra. For superstrings, it is the orthosymplectic algebra that appears instead, with its lowest weight states forming the simplest class of physical trajectories in the NS sector. To construct the simplest class in the R sector, the lowest weight states need to be supplemented with other states, which we determine. Deeper trajectories are then constructed by acting with suitable combinations of the raising operators of the orthosymplectic algebra, which we illustrate with several examples.

Pions from higher-dimensional gluons: general realizations and stringy models

In this paper we revisit the general phenomenon that scattering amplitudes of pions can be obtained from “dimensional reduction” of gluons in higher dimensions in a more general context. We show that such “dimensional reduction” operations universally turn gluons into pions regardless of details of interactions: under such operations any amplitude that is gauge invariant and contains only local simple poles becomes one that satisfies Adler zero in the soft limit. As two such examples, we show that starting from gluon amplitudes in both superstring and bosonic string theories, the operations produce “stringy” completion of pion scattering amplitudes to all orders in α′, with leading order given by non-linear sigma model amplitudes. Via Kawai-Lewellen-Tye relations, they give closed-stringy completion for Born-Infeld theory and the special Galileon theory, which are directly related to gravity amplitudes in closed-string theories. We also discuss how they naturally produce stringy models for mixed amplitudes of pions and colored scalars.

Effective interactions of the open bosonic string via field theory

We describe a method to extract an effective Lagrangian description for open bosonic strings, at zero transcendentality. The method relies on a particular formulation of its scattering amplitudes derived from color-kinematics duality. More precisely, starting from a (DF)2 + YM quantum field theory, we integrate out all the massive degrees of freedom to generate an expansion in the inverse string tension α′. We explicitly compute the Lagrangian terms through O\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O} $$\\end{document}(α′4), and target the sector of operators proportional to F4 to all orders in α′.

Veneziano and Shapiro-Virasoro amplitudes of arbitrarily excited strings

We extend the Veneziano and Shapiro-Virasoro amplitudes to four arbitrarily excited states in bosonic string theory. We use the formalism of coherent string states based on the Di Vecchia-Del Giudice-Fubini construction. Within the same formalism, we also analyze the three string scattering finding the covariant version of the three reggeon interaction. Then studying the factorization properties of the extended four string scattering amplitudes we identify the covariant version of the three string interaction. Finally we obtain generalized Kawai-Lewellen-Tye relations connecting the scattering of four open and closed arbitrarily excited states.

Engineering perturbative string duals for symmetric product orbifold CFTs

Constructing a holographic string theory dual for a CFT in the perturbative, weakly coupled regime is a holy grail for gauge/string dualities that would not only open the door for proofs of the AdS/CFT correspondence but could also provide novel examples of string duals with and without supersymmetry. In this work we consider some marginal perturbation of a family of symmetric product orbifolds in two dimensions. From their correlation functions we engineer a bosonic string theory whose amplitudes are shown to reproduce the CFT correlation function order-by-order both in the coupling and in 1/N. Our derivation does not require to compute and compare correlation functions explicitly but rather relies on a sequence of identities that can be derived using path integral methods. The bosonic string theory we engineer is based on the field content of the Kac-Wakimoto representation of strings in AdS3 with k units of pure NSNS flux, but the interaction terms we obtain are different. They include current algebra preserving interaction terms with one unit of spectral flow.

Tensionless strings in a Kalb-Ramond background

We investigate tensionless (or null) bosonic string theory with a Kalb-Ramond background turned on. In analogy with the tensile case, we find that the Kalb-Ramond field has a non-trivial effect on the spectrum only when the theory is compactified on an (S1)⊗d background with d ≥ 2. We discuss the effect of this background field on the tensionless spectrum constructed on three known consistent null string vacua. We elucidate further on the intriguing fate of duality symmetries in these classes of string theories when the background field is turned on.

The bubble of nothing under T-duality

The bubble of nothing is a solution to Einstein’s equations where a circle shrinks and pinches off smoothly. As such, it is one of the simplest examples of a dynamical cobordism to nothing. We take a first step in studying how this solution transforms under T-duality in bosonic string theory. Applying Buscher’s rules reveals that the dual solution features a singular, strongly coupled core, with a circle blowing-up rather than pinching off. This naive approach to T-duality solely accounts for the zero-modes of the fields after dimensional reduction on the circle. For this reason, we argue that this is not the full picture that the T-dual solution should depend non-trivially on the dual circle. We point out evidence to this effect both in the gravity description and on the worldsheet. A more complete description of the T-dual object would require a full-fledged sigma model for the bubble of nothing. Nevertheless, inspired by similar examples in the literature, we detail one possible scenario where the stringy bubble of nothing is mediated by closed string tachyon condensation and we discuss its T-duality.

Basis decompositions of genus-one string integrals

One-loop scattering amplitudes in string theories involve configuration-space integrals over genus-one surfaces with coefficients of Kronecker-Eisenstein series in the integrand. A conjectural genus-one basis of integrands under Fay identities and integration by parts was recently constructed out of chains of Kronecker-Eisenstein series. In this work, we decompose a variety of more general genus-one integrands into the conjectural chain basis. The explicit form of the expansion coefficients is worked out for infinite families of cases where the Kronecker-Eisenstein series form cycles. Our results can be used to simplify multiparticle amplitudes in supersymmetric, heterotic and bosonic string theories and to investigate loop-level echoes of the field-theory double-copy structures of string tree-level amplitudes. The multitude of basis reductions in this work strongly validate the recently proposed chain basis and stimulate mathematical follow-up studies of more general configuration-space integrals with additional marked points or at higher genus.

Thermal Bekenstein-Hawking entropy from the worldsheet

We define and compute the leading sphere diagram contribution to the entropy of the BTZ black hole supported by Kalb-Ramond flux in bosonic string theory. In a winding condensate description, integrating exactly over the constant mode for the radial direction of AdS3 reduces the problem to one of the correlation functions of winding operators in the free theory. The volume of the residual PSL(2,ℂ) gauge group of the sphere is canceled by the action of conformal transformations on the winding interaction insertions. We formulate a precise version of the replica trick in terms of (infinitesimally) non-integer winding condensates to produce the entropy of the BTZ black hole. The resulting entropy can be calculated from the one-point function of a non-local operator on the worldsheet.

Massive Strings from a Field Theory with Ghosts.

In this Letter, we present the α^{'}-exact background equations of motion of the bosonic chiral string (also known as Hohm-Siegel-Zwiebach model), with the spin-two ghost fields integrated out. This is the first instance of a world sheet model in which all corrections are fully determined in a generic curved spacetime. As a concrete cross-check, we find complete agreement between all three-point and a sample of four-point tree-level scattering amplitudes computed using field theory methods and the chiral string prescription. These equations of motion provide a field theoretical shortcut to compute world sheet correlators in conventional bosonic strings (with an arbitrary number of massless and mass-level-one states) and outline a new perspective on massive resonances in string theory.