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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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

We argue that on-shell excitations with large negative energies are created rapidly when the string coupling increases with time. This does not indicate an inconsistency in string theory since the negative energy on-shell excitation is always entangled with an on-shell excitation with a positive energy. The total energy of this energy-EPR state vanishes. We discuss the reason the energy-EPR states appear in string theory and the role they might play in black hole physics. [ABSTRACT FROM AUTHOR]

The known stringy non-relativistic (NR) limit of the universal NS-NS sector of supergravity has a finite Lagrangian due to non-trivial cancellations of divergent parts coming from the metric and the B-field. We demonstrate that in Double Field Theory (DFT) and generalised geometry these cancellations already happen at the level of the generalised metric, which is convergent in the limit c → ∞, implying that the NR limit can be imposed before solving the strong constraint. We present the c-expansion of the generalised metric, which reproduces the Non-Riemannian formulation of DFT at the (finite) leading order, and the c-expansion of the generalised frame, which contains divergences. We also extend this approach to the non-Abelian gauge field of Heterotic DFT assuming a convergent expansion for the O(D, D + n) generalised metric. From this proposal, we derive a novel c-expansion for the bosonic part of the heterotic supergravity which is, by construction, compatible with O(D, D)-symmetry. [ABSTRACT FROM AUTHOR]

We introduce a two parameter family of string field theory vertices, which we refer to as hyperbolic Kaku vertices. It is defined in terms of hyperbolic metrics on the Riemann surface, but the geometry is allowed to depend on inputs of the states. The vertices are defined for both open and closed strings. In either case, the family contains the hyperbolic vertices. Then we show that the open string lightcone vertex is obtained as the flat limit of the hyperbolic Kaku vertices. The open string Kaku vertices, which interpolate between the Witten vertex and the open string lightcone vertex, is also obtained as a flat limit. We use the same limit on the case of closed strings to define the closed string Kaku vertices: a one parameter family of vertices that interpolates between the polyhedral vertices — which are covariant, but not cubic — and the closed string lightcone vertex — which is cubic, but not Lorentz covariant. [ABSTRACT FROM AUTHOR]

Abstract 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.

Abstract In IIB string theory on AdS3 background with NS-NS fluxes, we show that Brown-Henneaux asymptotic Killing vectors can be derived by requiring both the worldsheet equations of motion and Virasoro constraints are preserved near the asymptotic boundary of the target spacetime. The charges on the worldsheet that generate the corresponding transformations can be written down in both the Lagrangian formalism and Hamiltonian formalism. This provides a method of studying asymptotic symmetry of the target spacetime directly from worldsheet string theories, without using results from the supergravity limit. As an example, we apply this method to flat spacetime in three dimensions and obtain the BMS3 generators on the worldsheet theory.

Abstract We argue that on-shell excitations with large negative energies are created rapidly when the string coupling increases with time. This does not indicate an inconsistency in string theory since the negative energy on-shell excitation is always entangled with an on-shell excitation with a positive energy. The total energy of this energy-EPR state vanishes. We discuss the reason the energy-EPR states appear in string theory and the role they might play in black hole physics.

Abstract 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.

Abstract We compute the tree-level connected six-point function of identical scalar fluctuations of the AdS2 string worldsheet dual to the half-BPS Wilson line in planar N $$ \mathcal{N} $$ = 4 Super Yang-Mills. The calculation can be carried out analytically in the conformal gauge approach, where the boundary reparametrization mode of the string plays a crucial role. We also study the analytic continuation of the six-point function to an out-of-time-order configuration, which is related to a 3-to-3 scattering amplitude in flat space. As a check of our results, we also numerically compute the six-point function using the Nambu-Goto action in static gauge, finding agreement with the conformal gauge answer.

Abstract This paper investigates the relationships between closed and mixed string amplitudes at the tree level in string theory. Through the analytic continuation of complex variables, we establish a factorization of closed string amplitudes into those involving (n − 2) open strings and a single closed string. Expressions for four-, five-, and six-point amplitudes are provided, together with systematic formulations for n-point string amplitudes. The paper addresses possible correction terms arising from integration along infinite tubes during the process of Wick rotations. The implications of our findings are discussed in certain limits.

Abstract Generalizing recent work by Schnabl-Stettinger and Erbin-Fırat, we outline a universal algebraic procedure for ‘adding stubs’ to string field theories obeying the BV quantum master equation. We apply our results to classical and quantum closed string field theory as well as to open-closed string field theory. We also clarify several aspects of the integration-out process in the co-algebraic formulation of string field theory at the quantum level.

Abstract The known stringy non-relativistic (NR) limit of the universal NS-NS sector of supergravity has a finite Lagrangian due to non-trivial cancellations of divergent parts coming from the metric and the B-field. We demonstrate that in Double Field Theory (DFT) and generalised geometry these cancellations already happen at the level of the generalised metric, which is convergent in the limit c → ∞, implying that the NR limit can be imposed before solving the strong constraint. We present the c-expansion of the generalised metric, which reproduces the Non-Riemannian formulation of DFT at the (finite) leading order, and the c-expansion of the generalised frame, which contains divergences. We also extend this approach to the non-Abelian gauge field of Heterotic DFT assuming a convergent expansion for the O(D, D + n) generalised metric. From this proposal, we derive a novel c-expansion for the bosonic part of the heterotic supergravity which is, by construction, compatible with O(D, D)-symmetry.

Abstract We introduce a two parameter family of string field theory vertices, which we refer to as hyperbolic Kaku vertices. It is defined in terms of hyperbolic metrics on the Riemann surface, but the geometry is allowed to depend on inputs of the states. The vertices are defined for both open and closed strings. In either case, the family contains the hyperbolic vertices. Then we show that the open string lightcone vertex is obtained as the flat limit of the hyperbolic Kaku vertices. The open string Kaku vertices, which interpolate between the Witten vertex and the open string lightcone vertex, is also obtained as a flat limit. We use the same limit on the case of closed strings to define the closed string Kaku vertices: a one parameter family of vertices that interpolates between the polyhedral vertices — which are covariant, but not cubic — and the closed string lightcone vertex — which is cubic, but not Lorentz covariant.

Abstract 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 $$ \mathcal{O} $$ (α′4), and target the sector of operators proportional to F 4 to all orders in α′.

Abstract We propose a novel indicator for chaotic quantum scattering processes, the scattering form factor (ScFF). It is based on mapping the locations of peaks in the scattering amplitude to random matrix eigenvalues, and computing the analog of the spectral form factor (SFF). We compute the spectral and scattering form factors of several non-chaotic systems. We determine the ScFF associated with the phase shifts of the leaky torus, closely related to the distribution of the zeros of Riemann zeta function. We compute the ScFF for the decay amplitude of a highly excited string states into two tachyons. We show that it displays the universal features expected from random matrix theory - a decline, a ramp and a plateau - and is in general agreement with the Gaussian unitary ensemble. It also shows some new features, owning to the special structure of the string amplitude, including a “bump” before the ramp associated with gaps in the average eigenvalue density. The “bump” is removed for highly excited string states with an appropriate state dependent unfolding. We also discuss the SFF for the Gaussian β-ensemble, writing an interpolation between the known results of the Gaussian orthogonal, unitary, and symplectic ensembles.

Abstract In this paper, we studied the relationship between celestial holography and chiral strings. Chiral strings differ from the usual string theory by a change of boundary conditions on the string propagators. It is shown that chiral strings would reproduce graviton amplitudes and could serve as an alternative description of Einstein’s gravity. Celestial holography is a proposed duality between gravity in asymptotically flat space-time and a CFT living on its conformal boundary. Since both are CFT descriptions of gravity, we investigate the potential connection between these two formalisms. In this paper, we find that both the energetic as well as conformal soft theorems could be derived from the OPEs of vertex operators of chiral strings. All operators in the CCFT can be described by Mellin transforming the vertex operators in the chiral string theories, and the OPE coefficients of CCFT can also be obtained from the world-sheet description.

Abstract 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.

Abstract 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 (S 1)⊗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.

Abstract 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.

Abstract In string theories, one-loop scattering amplitudes are characterized by integrals over genus-one surfaces using the Kronecker-Eisenstein series. A recent methodology proposed a genus-one basis formed from products of these series of chain topologies. A prior work further deconstructed cyclic products of the Kronecker-Eisenstein series on this basis. Building on it, our study further employs advanced and comprehensive combinatorial techniques to decompose more general genus-one integrands including a product of an arbitrary number of cyclic products of Kronecker-Eisenstein series, supplemented by Mathematica codes. Our insights enhance the understanding of multiparticle amplitudes across various string theories and illuminate loop-level parallels with string tree-level amplitudes.

Abstract 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.

Abstract 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.

Abstract Starting from the Polyakov action we consider two distinct Carroll limits in target space, keeping the string worldsheet relativistic. The resulting magnetic and chiral Carroll string models exhibit different symmetries and dynamics. Both models have an infinite dimensional symmetry algebra with Carroll symmetry included in a finite dimensional subalgebra. For the magnetic model, this is the so-called string Carroll algebra. The chiral model realises an extended version of the string Carroll algebra. The magnetic model does not have any transverse string excitations. The chiral model is less restrictive and includes arbitrary left-moving modes that carry transverse momentum but do not contribute to the energy in target space.

Abstract We study string theory in three-dimensional Anti-de Sitter spacetime in the path integral formalism. We derive expressions for generic spectrally-flowed near-boundary vertex operators in the Wakimoto representation, and relate their correlation functions to covering maps from the worldsheet to the target space boundary. We show that the path integral structurally reproduces correlation functions of the dual symmetric orbifold theory. By rephrasing spectral flow as the introduction of a background gauge field, we provide a path integral derivation of the localisation property of the near boundary theory. We then focus on the case of IIB string theory on AdS3 × S3 × 𝕋4 with k = 1 units of NS-NS flux, where the relationship between correlation functions and covering maps can be made sharp. We also comment on the relation of the k = 1 theory and twistor theory.

Abstract We compute the spectra associated with various semiclassical string states that propagate over N $$ \mathcal{N} $$ = 2 Gaiotto-Maldacena backgrounds. As an interesting special case, for the Abelian T- dual solution, we discover giant magnon and single spike configurations while imposing appropriate boundary conditions. However, for Sfetsos-Thompson backgrounds, one has to adopt a different string embedding which reveals “modified” dispersion relations both for magnons and spikes. These results boil down into the standard dispersion relations in the limit when the rank of the associated SU(N c ) color gauge group becomes large enough. We further generalize our analysis in the presence of flavor D6 branes. Our analysis reveals a new set of dispersion relations, which shows that both magnons and spikes are ceased to exist in the presence of flavor excitations.

Abstract We utilize a novel method for the partial-wave unitarity recently suggested in [1] to analyse the hypergeometric Coon amplitude. In this approach we use a new type of harmonic numbers as a basis. Owing to the properties of the harmonic numbers this method bypasses lots of difficulties and can be used to derive a clear and unified form for the partial-wave coefficients. This new approach further streamlines the partial-wave unitarity analysis. As an instance, we re-derive the unitarity bounds from Regge trajectory analysis and find the new critical condition of the hypergeometric Coon amplitude. Our new method also benefits the discussion on the various limits of this amplitude. Specifically, we demonstrate the manifest positivity of super string below d ≤ 10 from our new perspective.

Abstract With the aim of investigating the existence of an integrable elliptic deformation of strings on AdS3 × S3 × T4, we compute the tree-level worldsheet S-matrix of the elliptically-deformed bosonic sigma model on AdS3 × S3 in uniform light-cone gauge. The resulting tree-level S-matrix is compatible with the integrability of the model and has interesting features, including a hidden U(1) symmetry not manifest in the Lagrangian. We find that it cannot be embedded in the known exact integrable R-matrices describing deformations of the undeformed AdS3 × S3 × T4 light-cone gauge S-matrix including fermions. Therefore, we construct embeddings of the deformed 6-d metric in type II supergravity with constant dilaton and homogeneous fluxes. The simplicity of these solutions suggests they are promising candidates to lead to an integrable string sigma model including fermions.

Abstract The geometry of 4-string contact interaction of closed string field theory is characterized using machine learning. We obtain Strebel quadratic differentials on 4-punctured spheres as a neural network by performing unsupervised learning with a custom-built loss function. This allows us to solve for local coordinates and compute their associated mapping radii numerically. We also train a neural network distinguishing vertex from Feynman region. As a check, 4-tachyon contact term in the tachyon potential is computed and a good agreement with the results in the literature is observed. We argue that our algorithm is manifestly independent of number of punctures and scaling it to characterize the geometry of n-string contact interaction is feasible.

Abstract We investigate the proposed holographic duality between the TsT transformation of IIB string theory on AdS3 × $$\mathcal{N}$$ with NS-NS flux and a single-trace $$T\overline{T }$$ deformation of the symmetric orbifold CFT. We present a non-perturbative calculation of two-point correlation functions using string theory and demonstrate their consistency with those of the $$T\overline{T }$$ deformation. The two-point correlation function of the deformed theory on the plane, written in momentum space, is obtained from that of the undeformed theory by replacing h with $$h+2\frac{\widetilde{\lambda }}{w}p\overline{p }$$ , where h is the spacetime conformal weight, $$\widetilde{\lambda }$$ is a deformation parameter, p and $$\overline{p }$$ are the momenta, and w labels the twisted sectors in the deformed symmetric product. At w = 1, the non-perturbative result satisfies the Callan-Symanzik equation for double-trace $$T\overline{T }$$ deformed CFT derived in [1]. We also perform conformal perturbations on both the worldsheet CFT and the symmetric orbifold CFT as a sanity check. The perturbative and non-perturbative matching between results on the two sides provides further evidence of the conjectured $${\text{TsT}}/T\overline{T }$$ correspondence.

Abstract We study the holographic interpretation of the bulk instability, i.e. the bulk Lyapunov exponent in the motion of open classical bosonic strings in AdS black hole/brane/string backgrounds. In the vicinity of homogeneous and isotropic horizons the bulk Lyapunov exponent saturates the MSS chaos bound but in fact has nothing to do with chaos as our string configurations live in an integrable sector. In the D1-D5-p black string background, the bulk Lyapunov exponent is deformed away from the MSS value both by the rotation (the infrared deformation) and the existence of an asymptotically flat region (the ultraviolet deformation). The dynamics is still integrable and has nothing to do with chaos (either in gravity or in field theory). Instead, the bulk Lyapunov scale captures the imaginary part of quasinormal mode frequencies. Therefore, the meaning of the bulk chaos is that it determines the thermal decay rate due to the coupling to the heat bath, i.e. the horizon.

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. [ABSTRACT FROM AUTHOR]

Starting from the Polyakov action we consider two distinct Carroll limits in target space, keeping the string worldsheet relativistic. The resulting magnetic and chiral Carroll string models exhibit different symmetries and dynamics. Both models have an infinite dimensional symmetry algebra with Carroll symmetry included in a finite dimensional subalgebra. For the magnetic model, this is the so-called string Carroll algebra. The chiral model realises an extended version of the string Carroll algebra. The magnetic model does not have any transverse string excitations. The chiral model is less restrictive and includes arbitrary left-moving modes that carry transverse momentum but do not contribute to the energy in target space. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

We study string theory in three-dimensional Anti-de Sitter spacetime in the path integral formalism. We derive expressions for generic spectrally-flowed near-boundary vertex operators in the Wakimoto representation, and relate their correlation functions to covering maps from the worldsheet to the target space boundary. We show that the path integral structurally reproduces correlation functions of the dual symmetric orbifold theory. By rephrasing spectral flow as the introduction of a background gauge field, we provide a path integral derivation of the localisation property of the near boundary theory. We then focus on the case of IIB string theory on AdS3 × S3 × 핋4 with k = 1 units of NS-NS flux, where the relationship between correlation functions and covering maps can be made sharp. We also comment on the relation of the k = 1 theory and twistor theory. [ABSTRACT FROM AUTHOR]

We compute the spectra associated with various semiclassical string states that propagate over N = 2 Gaiotto-Maldacena backgrounds. As an interesting special case, for the Abelian T- dual solution, we discover giant magnon and single spike configurations while imposing appropriate boundary conditions. However, for Sfetsos-Thompson backgrounds, one has to adopt a different string embedding which reveals “modified” dispersion relations both for magnons and spikes. These results boil down into the standard dispersion relations in the limit when the rank of the associated SU(Nc) color gauge group becomes large enough. We further generalize our analysis in the presence of flavor D6 branes. Our analysis reveals a new set of dispersion relations, which shows that both magnons and spikes are ceased to exist in the presence of flavor excitations. [ABSTRACT FROM AUTHOR]

In string theories, one-loop scattering amplitudes are characterized by integrals over genus-one surfaces using the Kronecker-Eisenstein series. A recent methodology proposed a genus-one basis formed from products of these series of chain topologies. A prior work further deconstructed cyclic products of the Kronecker-Eisenstein series on this basis. Building on it, our study further employs advanced and comprehensive combinatorial techniques to decompose more general genus-one integrands including a product of an arbitrary number of cyclic products of Kronecker-Eisenstein series, supplemented by Mathematica codes. Our insights enhance the understanding of multiparticle amplitudes across various string theories and illuminate loop-level parallels with string tree-level amplitudes. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

We utilize a novel method for the partial-wave unitarity recently suggested in [1] to analyse the hypergeometric Coon amplitude. In this approach we use a new type of harmonic numbers as a basis. Owing to the properties of the harmonic numbers this method bypasses lots of difficulties and can be used to derive a clear and unified form for the partial-wave coefficients. This new approach further streamlines the partial-wave unitarity analysis. As an instance, we re-derive the unitarity bounds from Regge trajectory analysis and find the new critical condition of the hypergeometric Coon amplitude. Our new method also benefits the discussion on the various limits of this amplitude. Specifically, we demonstrate the manifest positivity of super string below d ≤ 10 from our new perspective. [ABSTRACT FROM AUTHOR]

With the aim of investigating the existence of an integrable elliptic deformation of strings on AdS3 × S3 × T4, we compute the tree-level worldsheet S-matrix of the elliptically-deformed bosonic sigma model on AdS3 × S3 in uniform light-cone gauge. The resulting tree-level S-matrix is compatible with the integrability of the model and has interesting features, including a hidden U(1) symmetry not manifest in the Lagrangian. We find that it cannot be embedded in the known exact integrable R-matrices describing deformations of the undeformed AdS3 × S3 × T4 light-cone gauge S-matrix including fermions. Therefore, we construct embeddings of the deformed 6-d metric in type II supergravity with constant dilaton and homogeneous fluxes. The simplicity of these solutions suggests they are promising candidates to lead to an integrable string sigma model including fermions. [ABSTRACT FROM AUTHOR]

We study the holographic interpretation of the bulk instability, i.e. the bulk Lyapunov exponent in the motion of open classical bosonic strings in AdS black hole/brane/string backgrounds. In the vicinity of homogeneous and isotropic horizons the bulk Lyapunov exponent saturates the MSS chaos bound but in fact has nothing to do with chaos as our string configurations live in an integrable sector. In the D1-D5-p black string background, the bulk Lyapunov exponent is deformed away from the MSS value both by the rotation (the infrared deformation) and the existence of an asymptotically flat region (the ultraviolet deformation). The dynamics is still integrable and has nothing to do with chaos (either in gravity or in field theory). Instead, the bulk Lyapunov scale captures the imaginary part of quasinormal mode frequencies. Therefore, the meaning of the bulk chaos is that it determines the thermal decay rate due to the coupling to the heat bath, i.e. the horizon. [ABSTRACT FROM AUTHOR]

We investigate the proposed holographic duality between the TsT transformation of IIB string theory on AdS3 × with NS-NS flux and a single-trace deformation of the symmetric orbifold CFT. We present a non-perturbative calculation of two-point correlation functions using string theory and demonstrate their consistency with those of the deformation. The two-point correlation function of the deformed theory on the plane, written in momentum space, is obtained from that of the undeformed theory by replacing h with , where h is the spacetime conformal weight, is a deformation parameter, p and are the momenta, and w labels the twisted sectors in the deformed symmetric product. At w = 1, the non-perturbative result satisfies the Callan-Symanzik equation for double-trace deformed CFT derived in [1]. We also perform conformal perturbations on both the worldsheet CFT and the symmetric orbifold CFT as a sanity check. The perturbative and non-perturbative matching between results on the two sides provides further evidence of the conjectured correspondence. [ABSTRACT FROM AUTHOR]

The geometry of 4-string contact interaction of closed string field theory is characterized using machine learning. We obtain Strebel quadratic differentials on 4-punctured spheres as a neural network by performing unsupervised learning with a custom-built loss function. This allows us to solve for local coordinates and compute their associated mapping radii numerically. We also train a neural network distinguishing vertex from Feynman region. As a check, 4-tachyon contact term in the tachyon potential is computed and a good agreement with the results in the literature is observed. We argue that our algorithm is manifestly independent of number of punctures and scaling it to characterize the geometry of n-string contact interaction is feasible. [ABSTRACT FROM AUTHOR]

Abstract 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.

Abstract In perturbative string theory, one is generally interested in asymptotic observables, such as the S-matrix in flat spacetime, and boundary correlation functions in anti-de Sitter spacetime. However, there are backgrounds in which such observables do not exist. We study examples of such backgrounds in 1 + 1 dimensional string theory. In these examples, the Liouville wall accelerates and can become spacelike in the past and/or future. When that happens, the corresponding null infinity, at which the standard scattering states are defined, is shielded by the Liouville wall. We compute scattering and particle production amplitudes in these backgrounds in the region in parameter space where the wall remains timelike, and discuss the continuation of this picture to the spacelike regime. We also discuss the physics from the point of view of the dynamics of free fermions in backgrounds with a time-dependent Fermi surface.

Abstract We demonstrate the turbulent dynamics of the Nambu-Goto open string in the AdS3 spacetime. While the motion of a classical closed string in AdS is known to be integrable, the integrability of an open string motion depends on the boundary conditions at the string endpoints. We numerically solve the equations of motion of the open string under the boundary conditions where the endpoints are i) fixed to a finite radial coordinate in AdS, and ii) free. For i), we find turbulence on the string, that shows a cascade in the energy and angular momentum spectra. This result indicates the non-integrability of the open string with this type of boundary conditions. For ii), we find no turbulence. This is consistent with the integrability of the open string with the free boundary conditions.

Abstract In this work we consider heterotic-gravity as the low-energy approximation to heterotic string theory. We define a consistent non-relativistic limit of heterotic gravity that includes the Yang-Mills Chern-Simons term. We perform three tests on the heterotic limit: we use it to (i) derive the non-relativistic transformation rules, (ii) show the existence of a finite non-relativistic heterotic action and (iii) obtain the longitudinal non-relativistic T-duality rules. We show that in all these cases the limit procedure is well defined, free of divergences and leads to consistent non-trivial results. We comment on the interpretation of the T-duality rules in terms of a heterotic non-relativistic geometry underlying non-relativistic heterotic string theory.

Abstract We compute instanton corrections to the partition function of sine-Liouville (SL) theory, which provides a worldsheet description of two-dimensional string theory in a non-trivial tachyon background. We derive these corrections using a matrix model formulation based on a chiral representation of matrix quantum mechanics and using string theory methods. In both cases we restrict to the leading and subleading orders in the string coupling expansion. Then the CFT technique is used to compute two orders of the expansion in the SL perturbation parameter λ, while the matrix model gives results which are non-perturbative in λ. The matrix model results perfectly match those of string theory in the small λ expansion. We also generalize our findings to the case of perturbation by several tachyon vertex operators carrying different momenta, and obtain interesting analytic predictions for the disk two-point and annulus one-point functions with ZZ boundary condition.

Abstract We study the origin of turbulence on the string worldsheet with boundaries laid in anti de Sitter (AdS) spacetime. While the classical motion of a single closed string in AdS is integrable, it has recently been recognized that weak turbulence arises in the case of an open string suspended from the AdS boundary. In the open string case, it is necessary to impose boundary conditions on the worldsheet boundaries. We classify which boundary conditions preserve integrability. Based on this classification, we anticipate that turbulence may occur on the string worldsheet if integrability is not guaranteed by the boundary conditions. Numerical investigations of the classical open-string dynamics support that turbulence occurs when the boundary conditions are not integrable.

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. [ABSTRACT FROM AUTHOR]