String S-matrix Research Articles

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.

Weak chaos and mixed dynamics in the string S-matrix

We investigate chaotic dynamics in tree-level S-matrices describing the scattering of tachyons, photons and gravitons on highly excited open and closed bosonic strings, motivated by the string/black hole complementarity. The eigenphase spacing distribution and other indicators of quantum chaotic scattering suggest that the dynamics is only weakly chaotic, consisting of both regular/Poisson and chaotic/Wigner-Dyson processes. Only for special values of momenta and (for photon scattering) scattering angles do we find strong chaos of random matrix type. These special values correspond to a crossover between two regimes of scattering, dominated by short versus long partitions of the total occupation number of the highly excited string; they also maximize the information entropy of the S-matrix. The lack of strong chaos suggests that perturbative dynamics of highly excited strings can never describe the universal properties and maximal chaos of black hole horizons.

Thermal equilibrium in string theory in the Hagedorn phase

In string theory, a thermal state is described by compactifying Euclidean time on a thermal circle {S}_{beta}^1 , of fixed circumference. However, this circumference is a dynamical field which could vary in space, therefore thermal equilibrium is not guaranteed. We discuss a thermal state of type II string theory near and above the Hagedorn temperature and show that the circumference of the thermal circle can indeed be fixed and stabilized in the presence of a uniform isotropic flux. We solve the equations of motion derived from an action that reproduces the tree-level string S-matrix. We find solutions with the topologies of {S}_{beta}^1 × S2× mathcal{M} d−2 at a fixed temperature, which include a space-filling winding-mode condensate and a uniform Neveu-Schwarz Neveu-Schwarz flux supported on {S}_{beta}^1 × S2. The solutions that we find have either a linear dilaton or a constant dilaton, in which case, we find solutions with either a cosmological constant or a Ramond-Ramond flux. We then compare our solutions to the cigar and cylinder backgrounds associated with the SL(2, ℝ)/U(1) coset theory, which include a winding-mode condensate but without flux. We also compare and contrast our solutions with the non-uniform Horowitz-Polchinski solution, which also possesses a winding-mode condensate and is characterized by an approximate thermal equilibrium near the Hagedorn temperature.

The large- N Yang-Mills S matrix is ultraviolet finite, but the large- N QCD S matrix is only renormalizable

The solution of the large-N 't Hooft limit of QCD is universally believed to be a String Theory of Closed Strings in the Glueball Sector and of Open Strings in the Meson Sector. Yet, we prove a no-go theorem, that the large-N limit of QCD with massless quarks, or more generally, that the large-N limit of a vast class of confining, i.e. with a Mass Gap in the Glueball Sector, asymptotically-free Gauge Theories coupled to matter fields with no mass scale in perturbation theory cannot be a canonically-defined String Theory of Closed and Open Strings, i.e. admitting Open/Closed Duality. The no-go theorem occurs because Open/Closed Duality, implying that the ultraviolet divergences of annulus diagrams in the Open Sector arise from infrared divergences of tadpoles of massless particles in the Closed Sector, turns out to be incompatible with the existence of the Mass Gap in the Glueball Sector of confining asymptotically-free theories with no mass scale in perturbation theory in which, as for example in QCD, the first coefficient of the beta function for 't Hooft gauge coupling gets $1/N$ corrections due to the matter fields. Moreover, we suggest a way-out to the no-go theorem on the basis of a new non-canonical construction of the String S-matrix for asymptotically-free Gauge Theories such as large-N QCD, involving Topological Strings on Non-Commutative Twistor Space.

S-matrix for strings on η-deformed AdS5 × S5

We determine the bosonic part of the superstring sigma model Lagrangian on η-deformed AdS5 × S5, and use it to compute the perturbative world-sheet scattering matrix of bosonic particles of the model. We then compare it with the large string tension limit of the q-deformed S-matrix and find exact agreement.

Restoring unitarity in the q-deformed world-sheet S-matrix

The world-sheet S-matrix of the string in AdS5 x S5 has been shown to admit a q-deformation that relates it to the S-matrix of a generalization of the sine-Gordon theory, which arises as the Pohlmeyer reduction of the superstring. Whilst this is a fascinating development the resulting S-matrix is not explicitly unitary. The problem has been known for a long time in the context of S-matrices related to quantum groups. A braiding relation often called "unitarity" actually only corresponds to quantum field theory unitarity when the S-matrix is Hermitian analytic and quantum group S-matrices manifestly violate this. On the other hand, overall consistency of the S-matrix under the bootstrap requires that the deformation parameter is a root of unity and consequently one is forced to perform the "vertex" to IRF, or SOS, transformation on the states to truncate the spectrum consistently. In the IRF formulation unitarity is now manifest and the string S-matrix and the S-matrix of the generalised sine-Gordon theory are recovered in two different limits. In the latter case, expanding the Yang-Baxter equation we find that the tree-level S-matrix of the Pohlmeyer-reduced string should satisfy a modified classical Yang-Baxter equation explaining the apparent anomaly in the perturbative computation. We show that the IRF form of the S-matrix meshes perfectly with the bootstrap equations.

Coordinate Bethe ansatz for the string S-matrix

We use the coordinate Bethe ansatz approach to derive the nested Bethe equations corresponding to the recently found S-matrix for strings in AdS5 × S5, compatible with centrally extended symmetry.

ON THE SCATTERING PHASE FOR AdS5 × S5 STRINGS

We propose a phase factor of the worldsheet S-matrix for strings on AdS5 × S5 apparently solving Janik's crossing relation exactly.

Non-perturbative formulation of time-dependent string solutions

We formulate here a new world-sheet renormalization-group technique for the bosonic string, which is non-perturbative in the Regge slope alpha' and based on a functional method for controlling the quantum fluctuations, whose magnitudes are scaled by the value of alpha'. Using this technique we exhibit, in addition to the well-known linear-dilaton cosmology, a new, non-perturbative time-dependent background solution. Using the reparametrization invariance of the string S-matrix, we demonstrate that this solution is conformally invariant to alpha', and we give a heuristic inductive argument that conformal invariance can be maintained to all orders in alpha'. This new time-dependent string solution may be applicable to primordial cosmology or to the exit from linear-dilaton cosmology at large times.

Integrability and non-perturbative effects in the AdS/CFT correspondence

We present a non-perturbative resummation of the asymptotic strong-coupling expansion for the dressing phase factor of the AdS5 × S5 string S-matrix. The non-perturbative resummation provides a general form for the coefficients in the weak-coupling expansion, in agreement with crossing symmetry and transcendentality. The ambiguities of the non-perturbative prescription are discussed together with the similarities with the non-perturbative definition of the c = 1 matrix model.

A crossing–symmetric phase forAdS5×S5strings

We propose an all-order perturbative expression for the dressing phase of the AdS_5 x S^5 string S-matrix at strong coupling. Moreover, we are able to sum up large parts of this expression. This allows us to start the investigation of the analytic structure of the phase at finite coupling revealing a few surprising features. The phase obeys all known constraints including the crossing relation and it matches with the known physical data at strong coupling. In particular, we recover the bound states of giant magnons recently found by Hofman and Maldacena as poles of the scattering matrix. At weak coupling our proposal seems to differ with gauge theory. A possible solution to this disagreement is the inclusion of additional pieces in the phase not contributing to crossing, which we also study.

On AdS5×S5 string S-matrix

Recently two interesting conjectures about the string S-matrix on AdS5 × S 5 have been made. First, assuming the existence of a Hopf algebra symmetry Janik derived a functional equation for the dressing factor of the quantum string Bethe ansatz. Second, Hernandez and Lopez proposed an explicit form of 1/ √ λ correction to the dressing factor. In this Letter we show that in the strong coupling expansion Janik’s equation is solved by the dressing factor up to the order of its validity. This observation provides a strong evidence in favor of a conjectured Hopf algebra symmetry for strings in AdS5 × S 5 as well as the perturbative string S-matrix.

A matrix model for the null-brane

The null-brane background is a simple smooth 1/2 BPS solution of string theory. By tuning a parameter, this background develops a big crunch/big bang type singularity. We construct the DLCQ description of this space-time in terms of a Yang-Mills theory on a time-dependent space-time. Our dual Matrix description provides a non-perturbative framework in which the fate of both (null) time, and the string S-matrix can be studied.

Closed String S-matrix Elements in Open String Field Theory

We study the S-matrix elements of the gauge invariant operators corresponding to on-shell closed strings, in open string field theory. In particular, we calculate the tree level S-matrix element of two arbitrary closed strings, and the S-matrix element of one closed string and two open strings. By mapping the world-sheet of these amplitudes to the upper half z-plane, and by evaluating explicitly the correlators in the ghost part, we show that these S-matrix elements are exactly identical to the corresponding disk level S-matrix elements in perturbative string theory.

Strong evidence in favor of the existence of S-matrix for strings in plane waves

Field theories on the plane wave background are considered. We discuss that for such field theories one can only form 1+1 dimensional freely propagating wave packets. We analyze tree level four point functions of scalar field theory as well as scalars coupled to gauge fields in detail and show that these four point functions are well-behaved so that they can be interpreted as S-matrix elements for 2 particle $\to$ 2 particle scattering amplitudes. Therefore, at least classically, field theories on the plane wave background have S-matrix formulation.

Sigma model approach to string theory effective actions with tachyons

Motivated by recent discussions of actions for tachyon and vector fields related to tachyon condensation in open string theory we review and clarify some aspects of their derivation within the sigma model approach. In particular, we demonstrate that the renormalized partition function Z(T,A) of the boundary sigma model gives the effective action for massless vectors which is consistent with the string S-matrix and beta function, resolving an old problem with this suggestion in the bosonic string case at the level of the leading F2(dF)2 derivative corrections to Born–Infeld action. We give a manifestly gauge invariant definition of Z(T,A) in non-Abelian NSR open string theory and check that its derivative reproduces the tachyon beta function in a particular scheme. We also discuss the derivation of similar actions for tachyon and massless modes in closed bosonic and NSR (type 0) string theories. In the bosonic case the tachyon potential has the structure −T2e−T, but it vanishes in the NSR string case.

Recursion relation for the string S-matrix

We derive a recursion relation of the S-matrix for the open bosonic string by using the Witten string field theory. This relation is derived from a constraint equation analogous to the Virasoro constraints of the τ-function in the matrix model or topological gravity. This constraint equation may give the non-perturbative string S-matrix in non-trivial background fields.

Virasoro-Shapiro from Wilson

We develop the proposal of Banks and Martinec that the string field equation can be written as an infinite dimensional renormalization group equation. We generalize the Wilson equation to conformal invariance and to open strings, and make a preliminary study of the gauge invariance and auxiliary fields. To obtain the S-matrix, we first study the relatiion between field equations and S-matrices in general field theories. We then give a general demonstration that the field equations from world-sheet conformal invariance agree with the string S-matrix at tree level.

Order α′2 terms in the gravitational sector of string effective actions with the inclusion of the dilaton field

We discuss field redefinition ambiguities in string effective actions at order α ′2, in the parameterization which is most suitable for comparison with the string amplitudes and the σ-model parameterization. We find that, when the dilaton field is included, the effective action can be most simply described by seven terms, whose coefficients can be fixed from the string S-matrix. We derive relations among the coefficients that appear in each of the above mentioned parameterizations.

The heterotic σ-model with background gauge fields

We develop methods for simplifying considerably the computation of β-functions for the heterotic σ-model in the presence of background gauge fields. These methods are used to obtain three-loop results. Up to the overall normalization of the O(α- ′2) contribution, the β-functions are on-shell equivalent to the equations of motion derived from an effective action which has been obtained previously in the string S-matrix approach. Our results shed, however, new light on the off-shell relation between these field equations and the β-functions. It is also shown that, to all orders in α′, the net effect of gauge anomalies is the addition of a Chern-Simons term to the torsion.