We present a new method, exact in $α'$, to explicitly compute string tree-level amplitudes involving one massive state and any number of massless ones. This construction relies on the so-called twisted heterotic string, which admits only gauge multiplets, a gravitational multiplet, and a single massive supermultiplet in its spectrum. In this simplified model, we determine the moduli-space integrand of all amplitudes with one massive state using Berends-Giele currents of the gauge multiplet. These integrands are then straightforwardly mapped to gravitational amplitudes in the twisted heterotic string and to the corresponding massive amplitudes of the conventional type-I and type-II superstrings.
We discuss constructions of string vacua with a novel Massive boson-fermion Degeneracy Symmetry (MSDS) as candidate vacua able to describe the early non-geometrical era of the universe. Based on a talk given at the Workshop on Cosmology & Strings, Corfu Institute, Greece, Sept 12, 2009.
It is shown that all bosonic and fermionic massive string models admit consistent light-cone formulations. This result is used to derive the spin generating functions of these models in four dimensions.
We discuss marginal deformations of string vacua with Massive boson-fermion Degeneracy Symmetry (MSDS), in connection to the cosmological evolution of the Universe from an early non-geometrical era. In particular, we discuss recent results on the stringy mechanism that resolves both Hagedorn divergences and the Initial Singularity problem. Based on a talk given at the Workshop on Cosmology & Strings, Corfu Institute, Greece, Sept 10, 2010.
The massive IIA string theory whose low energy limit is the massive supergravity theory constructed by Romans is obtained from M-theory compactified on a 2-torus bundle over a circle in a limit in which the volume of the bundle shrinks to zero. The massive string theories in 9-dimensions given by Scherk-Schwarz reduction of IIB string theory are interpreted as F-theory compactified on 2-torus bundles over a circle. The M-theory solution that gives rise to the D8-brane of the massive IIA theory is identified. Generalisations of Scherk-Schwarz reduction are discussed.
We consider the sigma-model description of an open string interacting with massive fields of the fourth (third massive) level. Equations of motion for the background fields are obtained by demanding that the renormalized operator of the energy-momentum tensor trace vanishes.
We consider the theory of open bosonic string in massive background fields. The general structure of renormalization is investigated. A general covariant action for a string in background fields of the first massive level is suggested and its symmetries are described. Equations of motion for the background fields are obtained by demanding that the renormalized operator of the energy-momentum tensor trace vanishes.
In this report we obtain explicit string-like solutions of equations of motion of massive heterotic supergravity recently obtained by Bergshoeff, Roo and Eyras. We also find consistent string source which can be embedded in these backgrounds when space-time dimension is greater than or equal to six.
A systematic scheme is developed for solving conformal algebra of the massive vertex operators in the old covariant first quantized string theory. Using the first massive level in the covariant spectrum of bosonic open string theory in flat space-time as an example, we explicitly verify the conformal algebra for the normal-ordered covariant vertex operator. We emphasize that the requirement of fully covariant gauge-fixing specifies the form of normal-ordering for massive vertex operators.
We present evidence for the target space duality symmetry associated with massive excited states of closed bosonic string. The evolution of string is considered in ${\hat D}$ spacetime dimensions; out of which d spacial dimensions are compactified on torus. The phase space Hamiltonian formulation is adopted to unveil the T-duality symmetry from the worldsheet perspective. The existence of this symmetry is verified for a few massive levels. A systematic procedure is presented to study T-duality symmetry of vertex operators for all massive levels of closed bosonic string. It is argued that all v…
We calculate the semi-inclusive decay rate of an average string state with toroidal compactification in the the superstring theory. We also apply this calculation to a brane-inflation model in a warped geometry and find that the decay rate is greatly suppressed if the final strings are both massive and enhanced for massless radiation.
We briefly discuss the soft behavior of scattering amplitudes both in string and quantum field theory. In particular we show a general argument about the validity of soft theorems for open superstring amplitudes and list some of our recent results.
We calculate bosonic open string one-loop massive scattering amplitudes for some low-lying string states. By using the periodicity relations of Jacobi theta functions, we explicitly prove an infinite number of one-loop type I stringy Ward identities derived from type I zero-norm states in the old covariant first quantized (OCFQ) spectrum of open bosonic string. The subtlety in the proofs of one-loop type II stringy Ward identities is discussed by comparing with those of string-tree cases. High-energy limit of these stringy Ward identities can be used to fix the proportionality constants betwee…
We study the Casimir effect for a massive bosonic string terminating on D-brains, and living in a flat space with an antisymmetric background B-field. We find the Casimir energy and Casimir force as functions of the mass and length of the string and show the force does not depend on B-field. We also find the divergent part of the vacuum state energy, as a function of the mass and length of the string and offer an idea for renormalization of the mass of the string.
We calculate the semi-inclusive decay rate of an average string state with compactification both in the bosonic string theory and in the superstring theory. We also apply this calculation to a brane-inflation model in a warped geometry and find that the decay rate is greatly suppressed if final strings are all massive and enhanced with one final string massless, which may pose a challenge to this class of models.
We discuss a rigid string model proposed by Casalbuoni and Longhi. Constraints for the massive states are solved to find the physical states and the mass spectrum. We also find its supersymmetric extension with the kappa symmetry. The supersymmetry transformations are found starting from on-shell transformations using the Dirac bracket.
We study the BPS spectrum of four dimensional N=2 SU(2) theory with massive fundamental matters using the D3-brane probe. Since the BPS states are realized by string webs subject to the BPS conditions, we determine explicitly the configurations of such webs. It is observed that there appear BPS string webs with multiple of junctions corresponding to the fact that the curves of marginal stability in massive theory are infinitely nested. In terms of the string configurations, various properties of the curves of marginal stability are explained intuitively.
It is shown that the critical (or deconfinement) temperature for the Nambu-Goto string connecting the point-like masses (quarks) does not depend on the value of these masses. This temperature turns out to be the same as that in the case of string with fixed ends (infinitely heavy immobile quarks).
The loop variable approach used earlier to obtain free equations of motion for the massive modes of the open string, is generalized to include interaction terms. These terms, which are polynomial, involve only modes of strictly lower mass. Considerations based on operator product expansions suggest that these equations are particular truncations of the full string equations. The method involves broadening the loop to a band of finite thickness that describes all the different interacting strings. Interestingly, in terms of these variables, the theory appears non-interacting.
In the given work we study an interaction of second massive state of an open boson string with the constant electromagnetic field. This state contains massive fields with spins 3 and 1. Using the method of an open string BRST quantization, we receive gauge-invariant lagrangian, describing the electromagnetic interaction of these fields. From the explicit view of transformations and lagrangian it follows that the presence of external constant e/m field leads to the mixing of the given level states. Most likely that the presence of the external field will lead to the mixing of the states at othe…
A method of constructing a canonical gauge invariant quantum formulation for a non-gauge classical theory depending on a set of parameters is advanced and then applied to the theory of closed bosonic string interacting with massive background fields. Choosing an ordering prescription and developing a suitable regularization technique we calculate quantum guage algebra up to linear order in background fields. Requirement of closure for the algebra leads to equations of motion for massive background fields which appear to be consistent with the structure of string spectrum.
We propose a Matrix Theory approach to Romans' massive Type IIA supergravity. It is obtained by applying the procedure of Matrix Theory compactifications to Hull's proposal of the Massive Type IIA String Theory as M-Theory on a twisted torus. The resulting Matrix Theory is a super-Yang Mills theory on large N three-branes with a space dependent non-commutativity parameter, which is also independently derived by a T-duality approach. We give evidence showing that the energies of a class of physical excitations of the super-Yang Mills theory show the correct symmetry expected from Massive Type I…
We discuss the soft behaviour of open string amplitudes with gluons and massive states in any dimension. Notwithstanding non-minimal couplings of massive higher spin states to gluons, relying on OPE and factorization, we argue that the leading and sub-leading terms are universal and identical to the ones in Yang-Mills theories. In order to illustrate this, we compute some 4-point amplitudes on the disk involving gluons, massive states and, for the bosonic string, tachyons. For the superstring, we revisit the structure of the massive super-multiplets at the first massive level and rewrite the a…
We study the Casimir effect for a bosonic string extended between D-branes, and living in a flat space with an antisymmetric background B-field. We find the Casimir energy as a function of theB-field, and the mass-parameter of the string, and accordingly we obtain a B-dependence correction term to the ground-state mass of the string. We show that for sufficiently large B-field, the ground state of the string contains real (i.e. non-Tachyonic) particles.
In this work we study various aspects of six-dimensional ${\cal N}=(1,0)$ SCFTs. We consider the construction of their string duals in Massive IIA and discuss some observables in given examples. We study the dynamics of string solitons wrapping and rotating on the Massive IIA background and show that the associated Hamiltonian system is both non-integrable and chaotic, implying the non-integrability of the dual CFT. Our procedure is analytic, using well developed mathematical techniques, and numerical, by the explicit calculation of power spectra, Lyapunov coefficients and Poincaré sections.
Massive type IIA supergravity admits a warped AdS_6 x S^4 vacuum solution, which is expected to be dual to an N=2, D=5 super-conformal Yang-Mills theory. We study solutions for strings rotating or spinning in this background. The warp factor plays no essential role when the string spins in the AdS_6, implying a commonality in the leading Regge trajectories between the D=4 and D=5 super-conformal field theories. The warp factor does, however, become important when the string rotates in the S^4, in particular for long strings, which have the the relation E- 3J/2=c_1 + c_2/J^5+..., where the angu…
We give the details of symplectic quantization for a system containing second class constraints. This method is appropriate for imposing infinite series of constraints due to the boundary conditions. We use this method for massive bosonic strings in a background B-field and find the correct expansions of the fields in terms of the physical modes. We have found a canonical basis for this model.
The Romans type IIA supergravity allows fundamental strings to have explicit mass term at the tree level. We show that there exists a (F1,D2,D8) brane configuration which gives rise to $Lif_4^{(2)}\times {R}^1\times S^5$ vacua supported by the massive strings. The presence of D8-branes naturally excites massive fundamental strings. A compactification on circle relates these Lifshitz massive type-IIA background with the axion-flux $Lif_4^{(2)}\times {S}^1\times S^5$ vacua in ordinary type-IIB theory. The massive T-duality in eight dimensions further relates them to yet another $\widetilde{Lif}_…
An example of a consistent theory with massive higher spin fields is constructed in flat space-time of dimension three. The action is written in the light-cone gauge. The theory has certain stringy features, e.g. its spectrum is unbounded in spin and mass, the theory admits Chan-Paton factors. The quartic and the higher tree-level amplitudes vanish, which softens the UV behaviour at the loop level and provides a new mechanism of how massive higher spin states can resolve the Quantum Gravity Problem.
We study numerically the gravitational field of a star made of massive and neutral string states for the case in which the dilaton is massive. The solution exhibits very simple scaling properties in the dilaton mass. There is no horizon and the singularity is surrounded by a halo (the physical size of which is inversely proportional to the dilaton mass) where the scalar curvature is very large and proportional to the square of the dilaton mass.
We construct massive open string states around a classical solution in the oscillator formulation of Vacuum String Field Theory. In order for the correct mass spectrum to be reproduced, the projection operators onto the modes of the left- and right-half of the string must have an anomalous eigenvalue 1/2, and the massive states are constructed using the corresponding eigenvector. We analyze numerically the projection operators by regularizing them to finite size matrices and confirm that they indeed have eigenvalue 1/2. Beside the desired massive states, we have spurious massive as well as mas…
It is shown that the BRST resolution of the spaces of physical states of non-critical (anomalus) massive string models can be consistently defined. The appropriate anomalus complexes are obtained by canonical restrictions of the ghost extended spaces to the kernel of curvature operator and additional Gupta-Bleuler like conditions without any modifications of the matter sector. The cohomologies of the polarized anomalus complex are calculated and analyzed in details.
We extend our analysis of the soft behaviour of string amplitudes with massive insertions to closed strings at tree level (sphere). Relying on our previous results for open strings on the disk and on KLT formulae we check universality of the soft behaviour for gravitons to sub-leading order for superstring amplitudes and show how this gets modified for bosonic strings. At sub-sub-leading order we argue in favour of universality for superstrings on the basis of OPE of the vertex operators and gauge invariance for the soft graviton. The results are illustrated by explicit examples of 4-point amp…
The classical and the quantum massive string model based on a modified BDHP action is analyzed in the range of dimensions $1<d<25$. The discussion concerning classical theory includes a formulation of the geometrical variational principle, a phase-space description of the two-dimensional dynamics, and a detailed analysis of the target space geometry of classical solutions. The model is quantized using "old" covariant method. In particular an appropriate construction of DDF operators is given and the no-ghost theorem is proved. For a critical value of one of free parameters of the model the qua…
String-brane interactions provide an ideal framework to study the dynamics of the massive states of the string spectrum in a non-trivial background. We present here an analysis of tree-level amplitudes for processes in which an NS-NS string state from the leading Regge trajectory scatters from a D-brane into another state from the leading Regge trajectory, in general of a different mass, at high energies and small scattering angles. This is done by using world-sheet OPE methods and effective vertex operators. We find that this class of processes has a universal dependence on the energy of the …
We calculate bosonic massive closed string states at arbitrary mass levels scattered from Orientifold planes in the high-energy, fixed angle limit. For the case of O-particle scatterings, we obtain infinite linear relations among high-energy scattering amplitudes of different string states. We also confirm that there exist only closed string Regge poles in the form factor of the O-particle amplitudes as expected. For the case of O-domain-wall scatterings, we find that, like the well-known D-instanton scatterings, the amplitudes behave like field theory scatterings, namely UV power-law without …
Low-scale string models are phenomenological models in String Theory, in which the string scale M_s is of the order of TeV. String excited states which are characteristic modes in low-scale string models can be observed as resonances in dijet invariant mass distributions at the LHC. If a new heavy resonance is discovered at the LHC, it is important to investigate whether the resonance comes from low-scale string models. In this work, two analyses are performed: One is observing higher spin degeneracy of string excited states by an angular distribution analysis on the resonance, since the strin…
The first massive level of closed bosonic string theory is studied. Free-field equations are derived by imposing Weyl invariance on the world sheet. A two-parameter solution to the equation of motion and constraints is found in two dimensions with a flat linear-dilaton background. One-to-one tachyon scattering is studied in this background. The results support Dhar, Mandal and Wadia's proposal that 2D critical string theory corresponds to the c=1 matrix model in which both sides of the Fermi sea are excited.
We obtain a new-type of ${\cal N}=3$ Yang-Mills Chern-Simons theory from the Mukhi-Papageorgakis Higgsing of the ${\cal N}=3$ Gaiotto-Tomasiello theory. This theory has ${\cal N}=1$ BPS fuzzy funnel solution which is expressed in terms of the seven generators of SU(3), excluding $T_8$. We propose that this is an effective theory of multiple D2-branes with D6- and D8-branes background in massive IIA string theory.
A method of constructing a canonical gauge invariant quantum formulation for a non-gauge classical theory depending on a set of parameters is advanced and then applied to the theory of closed bosonic string interacting with massive background fields. It is shown that within the proposed formulation the correct linear equations of motion for background fields arise.
We calculate high energy massive string scattering amplitudes of open bosonic string in the Regge regime (RR). We found that the number of high energy amplitudes for each fixed mass level in the RR is much more numerous than that of Gross regime (GR) calculated previously. Moreover, we discover that the leading order amplitudes in the RR can be expressed in terms of the Kummer function of the second kind. In particular, based on a summation algorithm for Stirling number identity, we discover that the ratios calculated previously among scattering amplitudes in the GR can be extracted from this …
Derivations of consistent equations of motion for the massive spin two field interacting with gravity is reviewed. From the field theoretical point of view the most general classical action describing consistent causal propagation in vacuum Einstein spacetime is given. It is also shown that the massive spin two field can be consistently described in arbitrary background by means of lagrangian equations representing an infinite series in curvature. Within string theory equations of motion for the massive spin two field coupled to gravity is derived from the requirement of quantum Weyl invarianc…
We present two new solutions of Romans' massive type IIA supergravity characterized by the two non-trivial massive potentials of Romans' theory: the NSNS 2-form and the RR 7-form. They can be interpreted respectively as the intersection of a fundamental string and a D8-brane over a D0-brane and the intersection of a D6-brane with a D8-brane over a NSNS5-brane. The D8-brane manifests itself through the mass parameter and in the massless limit one recovers the standard fundamental string and D6-brane solutions. Although these solutions do not have the usual form for BPS bound states at threshold…
We propose various ways of adding mass terms to three-dimensional twistor string theory. We begin with a review of mini-twistor space--the reduction of D=4 twistor space to D=3. We adapt the two proposals for twistor string theory, Witten's and Berkovits's, to D=3 super Yang-Mills theory. In Berkovits's model, we identify the enhanced R-symmetry. We then construct B-model topological string theories that, we propose, correspond to D=3 Yang-Mills theory with massive spinors and massive and massless scalars in the adjoint representation of the gauge group. We also analyze the counterparts of the…
We find a general class of pp-wave solutions of type IIB string theory such that the light cone gauge worldsheet lagrangian is that of an interacting massive field theory. When the light cone Lagrangian has (2,2) supersymmetry we can find backgrounds that lead to arbitrary superpotentials on the worldsheet. We consider situations with both flat and curved transverse spaces. We describe in some detail the background giving rise to the N=2 sine Gordon theory on the worldsheet. Massive mirror symmetry relates it to the deformed $CP^1$ model (or sausage model) which seems to elude a purely supergr…
Topologically massive gravity (TMG) in three dimensions provides an interesting toy model for constructing a quantum theory of gravity. Although it can be thought of as standing as a theory in its own right, it is also of interest to see whether it can be described within the larger framework of string theory or M-theory. In this paper, we show that it can be embedded within the heterotic string, via a compactification on $S^3\times T^4$. Since all solutions of TMG can now be lifted to ten dimensions, this allows us to give a string and brane interpretation to quantities such as the central ch…
The closed relativistic string carrying a point-like mass in the space with nontrivial geometry is considered. For rotational states of this system (resulting in non-trivial Regge trajectories) the stability problem is solved. It was shown that rotations of the folded string with the massive point placed at the rotational center are stable (with respect to small disturbances) if the mass exceeds some critical value: $m>m_{cr}$. But these rotational states are unstable in the opposite case $m<m_{cr}$. We can treat this effect as the spontaneous symmetry breaking for the string state. Other clas…
The covariant operator quantization of the ordinary free spinning BDH string modified by adding the supersymmetric Liouville sector is analysed in the even target space dimensions $d=2,4,6,8$. The spectrum generating algebra for this model is constructed and a general version of the no-ghost theorem is proven. A counterpart of the GSO projection leads to a family of tachyon free unitary free string theories. One of these models is equivalent to the non-critical Rammond-Neveu-Schwarz spinning string truncated in the Neveu-Schwarz sector to the tachyon free eigenspace of the fermion parity opera…
The first string excited state can be observed as a resonance in dijet invariant mass distributions at the LHC, if the scenario of low-scale string with large extra dimensions is realized. A distinguished property of the dijet resonance by string excited states from that the other "new physics" is that many almost degenerate states with various spin compose a single resonance structure. It is examined that how we can obtain evidences of low-scale string models through the analysis of angular distributions of dijet events at the LHC. Some string resonance states of color singlet can obtain larg…
We make some remarks on possible definition of open string path integral in the presence of additional boundary couplings corresponding to the presence of masses at the ends of the string. These couplings are not conformally invariant implying that as in a non-critical string case one is to integrate over the 1d metric or reparametrizations of the boundary. We compute the partition function on the disc in the presence of an additional constant gauge field background and comment on the structure of the corresponding scattering amplitudes.
We calculate high energy massive scattering amplitudes of closed bosonic string compactified on the torus. For each fixed mass level with given quantized and winding momenta ((m/R),(1/2)nR), we obtain infinite linear relations among high energy scattering amplitudes of different string states. For some kinematic regimes, we discover that linear relations with N_{R}=N_{L} break down and, simultaneously, the amplitudes enhance to power-law behavior instead of the usual expoential fall-off behavior at high energies. It is the space-time T-duality symmetry that plays a role here. This result is co…
We calculate the NS-R fermionic zero-norm states of type II string spectrum. The massless and some possible massive zero-norm states are identified to be responsible for the space-time supersymmetry. The existence of other fermionic massive zero-norm states with higher spinor-tensor indices correspond to new enlarged boson-fermion symmetries of the theory at high energy. We also discuss the R-R charges and R-R zero-norm states and justify that perturbative string does not carry the massless R-R charges. However, the existence of some massive R-R zero-norm states make us speculate that string m…
We study the case of open string theory on a D1-brane in a critical electric field. It was argued in hep-th/0006085 that the massless open string modes of this theory decouple from the massive modes, corresponding to a decoupling of the U(1) degrees of freedom in the U(N) gauge theory dual. To provide further support for the decoupling, we present several examples of open string disk amplitudes. Because of the decoupling, many of the massive open string states are stable, indicating the presence of a number of correspondingly stable states in the gauge theory. We provide a lengthy list of thes…
In this work, we study the computational complexity of massive gravity theory via the "Complexity = Action" conjecture. Our system contains a particle moving on the boundary of the black hole spacetime. It is dual to inserting a fundamental string in the bulk background. Then this string would contribute a Nambu-Goto term, such that the total action is composed of the Einstein-Hilbert term, Nambu-Goto term and the boundary term. We shall investigate the time development of this system, and mainly discuss the features of the Nambu-Goto term affected by the graviton mass and the horizon curvatur…
We compute leading order quantum corrections to the Regge trajectory of a rotating string with massive endpoints using semiclassical methods. We expand the bosonic string action around a classical rotating solution to quadratic order in the fluctuations and perform the canonical quantization of the resulting theory. For a rotating string in $D$ dimensions the intercept receives contributions from $D-3$ transverse modes and one mode in the plane of rotation, in addition to a contribution due to the Polchinski-Strominger term of the non-critical effective string action when $D\neq26$. The interc…
We propose a method of constructing a gauge invariant canonical formulation for non-gauge classical theory which depends on a set of parameters. Requirement of closure for algebra of operators generating quantum gauge transformations leads to restrictions on parameters of the theory. This approach is then applied to bosonic string theory coupled to massive background fields. It is shown that within the proposed canonical formulation the correct linear equations of motion for background fields arise.
