String Worldsheet Research Articles

Spin gauge theory, duality and fermion pairing

We apply duality transformation to the Abelian Higgs model in 3+1 dimensions in the presence of electrons coupled to the gauge field. The Higgs field is in the symmetry broken phase, where flux strings can form. Dualization brings in an antisymmetric tensor potential Bμν, which couples to the electrons through a nonlocal interaction which can be interpreted as a coupling to the spin current. It also couples to the string worldsheet and gives rise to a string Higgs mechanism via the condensation of flux strings. In the phase where the Bμν field is massless, the nonlocal interaction implies a linearly rising attractive force between the electrons, which can be interpreted as the result of a pair of strings joining the electrons.

Asymptotically free AdS3/CFT2

We propose a new AdS3/CFT2 duality, in which the bulk string theory has a target spacetime AdS3 times a squashed three-sphere {mathbbm{S}}_{flat}^3 , and the dual CFT2 is a symmetric product of sigma models on ℝϕ× {mathbbm{S}}_{flat}^3 , deformed by a ϕ-dependent ℤ2 twist operator. The duality maps the asymptotic region of AdS3 to the region ϕ → ∞, where the twist interaction in the CFT2 turns off. The AdS3 backgrounds in question have RAdS< ℓs, and so lie on the string side of the string/black hole correspondence transition. As a consequence, the high energy density of states consists of a string gas in AdS3 rather than an ensemble of BTZ black holes. This property allows us to derive the dual CFT2 by a systematic analysis of the worldsheet string theory on AdS3.

The worldsheet dual of free super Yang-Mills in 4D

The worldsheet string theory dual to free 4d mathcal{N} = 4 super Yang-Mills theory was recently proposed in [1]. It is described by a free field sigma model on the twistor space of AdS5 × S5, and is a direct generalisation of the corresponding model for tensionless string theory on AdS3 × S3. As in the case of AdS3, the worldsheet theory contains spectrally flowed representations. We proposed in [1] that in each such sector only a finite set of generalised zero modes (‘wedge modes’) are physical. Here we show that after imposing the appropriate residual gauge conditions, this worldsheet description reproduces precisely the spectrum of the planar gauge theory. Specifically, the states in the sector with w units of spectral flow match with single trace operators built out of w super Yang-Mills fields (‘letters’). The resulting physical picture is a covariant version of the BMN light-cone string, now with a finite number of twistorial string bit constituents of an essentially topological worldsheet.

Entanglement entropy and edge modes in topological string theory. Part II. The dual gauge theory story

This is the second in a two-part paper devoted to studying entanglement entropy and edge modes in the A model topological string theory. This theory enjoys a gauge-string (Gopakumar-Vafa) duality which is a topological analogue of AdS/CFT. In part 1, we defined a notion of generalized entropy for the topological closed string theory on the resolved conifold. We provided a canonical interpretation of the generalized entropy in terms of the q-deformed entanglement entropy of the Hartle-Hawking state. We found string edge modes transforming under a quantum group symmetry and interpreted them as entanglement branes. In this work, we provide the dual Chern-Simons gauge theory description. Using Gopakumar-Vafa duality, we map the closed string theory Hartle-Hawking state to a Chern-Simons theory state containing a superposition of Wilson loops. These Wilson loops are dual to closed string worldsheets that determine the partition function of the resolved conifold. We show that the undeformed entanglement entropy due to cutting these Wilson loops reproduces the bulk generalized entropy and therefore captures the entanglement underlying the bulk spacetime. Finally, we show that under the Gopakumar-Vafa duality, the bulk entanglement branes are mapped to a configuration of topological D-branes, and the non-local entanglement boundary condition in the bulk is mapped to a local boundary condition in the gauge theory dual. This suggests that the geometric transition underlying the gauge-string duality may also be responsible for the emergence of entanglement branes.

Schwinger-Keldysh effective action for a relativistic Brownian particle in the AdS/CFT correspondence

We compute Schwinger-Keldysh effective action for a relativistic heavy quark (with constant background velocity) in strongly coupled N = 4 supersymmetric Yang-Mills plasma. The holographic dual description involves a noisy trailing string moving in Schwarzschild-AdS5 black brane. The noise is caused by Hawking radiation emitted from string worldsheet horizon. Besides quadractic terms, the effective action contains cubic interactions, which are entirely induced by the constant background velocity. The nonlinear fluctuation-dissipation relations for three-point functions are discussed based on holographic results.

Superconformal algebras for generalized Spin(7) and G2 connected sums

Worldsheet string theory compactified on exceptional holomony manifolds is revisited following [1], where aspects of the chiral symmetry were described for the case where the compact space is a 7-dimensional G2-holonomy manifold constructed as a Twisted Connected Sum. We reinterpret this result and extend it to Extra Twisted Connected Sum G2-manifolds, and to 8-dimensional Generalized Connected Sum Spin(7)-manifolds. Automorphisms of the latter construction lead us to conjecture new mirror maps.

On quantum deformations of AdS3 \xd7 S3 \xd7 T4 and mirror duality

We consider various integrable two-parameter deformations of the AdS3 × S3 × T4 superstring with quantum group symmetry. Working on the string worldsheet in light-cone gauge and to quadratic order in fermions, we obtain their common massive tree-level two-body S matrix, which matches the expansion of the conjectured exact q-deformed S matrix. We then analyze the behavior of the exact S matrix under mirror transformation — a double Wick rotation on the worldsheet — and find that it satisfies a mirror duality relation analogous to the distinguished q-deformed AdS5 × S5 S matrix in the one parameter deformation limit. Finally, we show that the fermionic q-deformed AdS5 × S5 S matrix also satisfies such a relation.

Scaling solutions of wiggly cosmic strings

Cosmic strings may have formed in the early universe due to the Kibble mechanism. While string networks are usually modeled as being of Nambu-Goto type, this description is understood to be a convenient approximation, which neglects the typically expected presence of additional degrees of freedom on the string worldsheet. Previous simulations of cosmic strings in expanding universes have established beyond doubt the existence of a significant amount of short-wavelength propagation modes (commonly called wiggles) on the strings, and a wiggly string extension of the canonical velocity-dependent one-scale model has been recently developed. Here we improve the physical interpretation of this model, by studying the possible asymptotic scaling solutions of this model, and in particular how they are affected by the expansion of the universe and the available energy loss or transfer mechanisms -- e.g., the production of loops and wiggles. In addition to the Nambu-Goto solution, to which the wiggly model reduces in the appropriate limit, we find that there are also solutions where the amount of wiggliness can grow as the network evolves or, for specific expansion rates, become a constant. Our results show that full scaling of the network, including the wiggliness, is much more likely in the matter era than in the radiation era, which is in agreement with numerical simulation results.

String correlators on AdS3: three-point functions

We revisit the computation of string worldsheet correlators on Euclidean AdS3 with pure NS-NS background. We compute correlation functions with insertions of spectrally flowed operators. We explicitly solve all the known constraints of the model and for the first time conjecture a closed formula for three-point functions with arbitrary amount of spectral flow. We explain the relation of our results with previous computations in the literature and derive the fusion rules of the model. This paper is the first in a series with several installments.

Wrapped fivebranes redux

The near-horizon region of Neveu-Schwarz fivebranes provides interesting examples of gauge/gravity duality. We revisit the structure of wrapped and/or intersecting fivebranes using the tools of null-gauged WZW models in worldsheet string theory, revealing the effective geometry of the fivebrane throat in a variety of examples. Variant gaugings yield linear dilaton fivebrane throats with AdS3 caps, providing a wealth of information about the near-BPS structure of the corresponding spacetime CFT duals.

Global conformal gauge in string theory

It was supposed for fifty years that the conformal gauge in string theory exists globally on the whole string world sheet. In fact, almost all results were obtained under this assumption. However, this statement was proved only locally in some neighbourhood of an arbitrary point on the worldsheet, and its extension is far from being obvious. In the present paper we prove that the conformal gauge does exists globally on the string worldsheet represented by an infinite strip with straight parallel boundaries.

Singularities of thermal correlators at strong coupling

We analyze the singularities of the two-point function in a conformal field theory at finite temperature. In a free theory, the only singularity is along the boundary light cone. In the holographic limit, a new class of singularities emerges since two boundary points can be connected by a nontrivial null geodesic in the bulk, encircling the photon sphere of the black hole. We show that these new singularities are resolved by tidal effects due to the black hole curvature, by solving the string worldsheet theory in the Penrose limit. Singularities in the asymptotically flat black hole geometry are also discussed.

Generalized velocity-dependent one-scale model for current-carrying strings

We develop an analytic model to quantitatively describe the evolution of superconducting cosmic string networks. Specifically, we extend the velocity-dependent one-scale (VOS) model to incorporate arbitrary currents and charges on cosmic string world sheets under two main assumptions, the validity of which we also discuss. We derive equations that describe the string network evolution in terms of four macroscopic parameters: the mean string separation (or, alternatively, the string correlation length) and the root mean square velocity which are the cornerstones of the VOS model, together with parameters describing the averaged timelike and spacelike current contributions. We show that our extended description reproduces the particular cases of wiggly and chiral cosmic strings, previously studied in the literature. This VOS model enables investigation of the evolution and possible observational signatures of superconducting cosmic string networks for more general equations of state, and these opportunities will be exploited in a companion paper.

Stringy canonical forms

Canonical forms of positive geometries play an important role in revealing hidden structures of scattering amplitudes, from amplituhedra to associahedra. In this paper, we introduce “stringy canonical forms”, which provide a natural definition and extension of canonical forms for general polytopes, deformed by a parameter α′. They are defined by real or complex integrals regulated with polynomials with exponents, and are meromorphic functions of the exponents, sharing various properties of string amplitudes. As α′→ 0, they reduce to the usual canonical form of a polytope given by the Minkowski sum of the Newton polytopes of the regulating polynomials, or equivalently the volume of the dual of this polytope, naturally determined by tropical functions. At finite α′, they have simple poles corresponding to the facets of the polytope, with the residue on the pole given by the stringy canonical form of the facet. There is the remarkable connection between the α′→ 0 limit of tree-level string amplitudes, and scattering equations that appear when studying the α′→ ∞ limit. We show that there is a simple conceptual understanding of this phenomenon for any stringy canonical form: the saddle-point equations provide a diffeomorphism from the integration domain to the interior of the polytope, and thus the canonical form can be obtained as a pushforward via summing over saddle points. When the stringy canonical form is applied to the ABHY associahedron in kinematic space, it produces the usual Koba-Nielsen string integral, giving a direct path from particle to string amplitudes without an a priori reference to the string worldsheet. We also discuss a number of other examples, including stringy canonical forms for finite-type cluster algebras (with type A corresponding to usual string amplitudes), and other natural integrals over the positive Grassmannian.

Long strings and symmetric product orbifold from the AdS3Bethe equations

A particularly rich class of integrable systems arises from the AdS/CFT duality. There, the two-dimensional quantum field theory living on the string worldsheet may be understood in terms of a non-relativistic factorized S matrix, and the energy spectrum may be derived by techniques such as the mirror thermodynamic Bethe ansatz or the quantum spectral curve. In the case of AdS3/CFT2 without Ramond-Ramond fluxes, the worldhseet theory is a Wess-Zumino-Witten model with continous and discrete representations which, for the lowest allowed level, is dual to the symmetric product orbifold of a free theory. I will show how continuous representations may arise from integrability, and that at the lowest level the Bethe equations yield the symmetric product orbifold partition function on the nose.

World-volume effective theories of locally non-geometric branes

We study world-volume effective theories of five-branes in type II string theories. We determine the bosonic zero-modes of the NS5-brane, the Kaluza-Klein monopole, the exotic Q5-, R5-branes and a space-filling brane, by direct calculations within the formalism of double field theory (DFT). We show that these zero-modes are Nambu-Goldstone modes associated with the spontaneously broken gauge symmetries in DFT. They are organized into the bosonic part of the six-dimensional mathcal{N} = (1) vector and the mathcal{N} = (2, 0) tensor multiplets. Among other things, we examine the locally non-geometric R5-branes and space-filling branes that are characterized by the winding space. We also study effective theories of five-branes with string worldsheet instanton corrections.

DGLA Dg and BV formalism

Differrential Graded Lie Algebra Dg was previously introduced in the context of current algebras. We show that under some conditions, the problem of constructing equivariantly closed form from closed invariant form is reduces to construction of a representation of Dg. This includes equivariant BV formalism. In particular, an analogue of intertwiner between Weil and Cartan models allows to clarify the general relation between integrated and unintegrated operators in string worldsheet theory.

S matrix for a three-parameter integrable deformation of AdS3 \xd7 S3 strings

We consider the three-parameter integrable deformation of the AdS3 × S3 superstring background constructed in arXiv:1811.00453. Working on the string worldsheet in uniform lightcone gauge, we find the tree-level bosonic S matrix of the model and study some of its limits.

Correlation functions of symmetric orbifold from AdS3 string theory

The paper examines correspondence among correlation functions of symmetric orbifold and string theory on AdS3 described by sl(2) Wess-Zumino-Novikov-Witten (WZNW) model. We start by writing down n-point function of twist operators in the symmetric orbifold in terms of the data of effective Riemann surface. It is then shown that the correlation function can be reproduced from the sl(2) WZNW model. The computation is based on the claim that string worldsheet is given by the same Riemann surface and the reduction method from sl(2) WZNW model to Liouville field theory. We first consider the genus zero surface and then generalize the analysis to the case of generic genus. The radius of AdS3 is related to the level k of the WZNW model. For k = 3, our result should be an important ingredient for deriving AdS3/CFT2 correspondence with tensionless superstrings to all orders in string perturbation theory. For generic k, relations involving specific forms of correlation functions for strings on AdS3× X were obtained.

Toward a 3d Ising model with a weakly-coupled string theory dual

It has long been expected that the 3d Ising model can be thought of as a string theory, where one interprets the domain walls that separate up spins from down spins as two-dimensional string worldsheets. The usual Ising Hamiltonian measures the area of these domain walls. This theory has string coupling of unit magnitude. We add new local terms to the Ising Hamiltonian that further weight each spin configuration by a factor depending on the genus of the corresponding domain wall, resulting in a new 3d Ising model that has a tunable bare string coupling g_sgs. We use a combination of analytical and numerical methods to analyze the phase structure of this model as g_sgs is varied. We study statistical properties of the topology of worldsheets and discuss the prospects of using this new deformation at weak string coupling to find a worldsheet description of the 3d Ising transition.