String Worldsheet Theory Research Articles

Chern-Simons theory, decomposition, and the A model

In this paper, we discuss how gauging one-form symmetries in Chern-Simons theories is implemented in an A-twisted topological open string theory. For example, the contribution from a fixed H/Z bundle on a three-manifold M, arising in a BZ gauging of H Chern-Simons, for Z a finite subgroup of the center of H, is described by an open string worldsheet theory whose bulk is a sigma model with target a Z-gerbe (a bundle of one-form symmetries) over T∗M, of characteristic class determined by the H/Z bundle. We give a worldsheet picture of the decomposition of one-form-symmetry-gauged Chern-Simons in three dimensions, and we describe how a target-space constraint on bundles arising in the gauged Chern-Simons theory has a natural worldsheet realization. Our proposal provides examples of the expected correspondence between worldsheet global higher-form symmetries, and target-space gauged higher-form symmetries.

NS5-brane backgrounds and coset CFT partition functions

Worldsheet string theory is solvable for a variety of backgrounds involving Neveu-Schwarz fivebranes, in terms of gauged nonlinear sigma models on group manifolds. We compute the worldsheet torus partition function of these models, and propose gauging of null isometries as a unifying principle and conceptual framework for this large family of string backgrounds. In the process, we explain how partition functions of asymmetrically gauged Wess-Zumino-Witten models can be computed from the path integral, and organize and systematize various results scattered throughout the literature.

Shock waves in holographic EPR pair

We study real-time correlators for N = 4 super Yang Mill fields coupled to a pair of entangled quarks using holography, in the setup that energy quanta sent from one quark perturb the quantum state of the fields and affect the other quark. We make the connection with the ER=EPR conjecture by considering the situation when two quarks are uniformly accelerating opposite to each other. The dynamics of quarks, in the gravity dual, is described by the string worldsheet theory, which in this case has the induced metric describing a two-sided AdS black hole, or a wormhole. Energy quanta sent by one of the quarks produce the shock wave on the worldsheet. We find the effect of shock wave on the boundary field correlators and we discuss the consequence for the ER=EPR conjecture.

AdS3 orbifolds, BTZ black holes, and holography

Conical defects of the form (AdS3 × S3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\mathbbm{S}}^3 $$\\end{document})/ℤk have an exact orbifold description in worldsheet string theory, which we derive from their known presentation as gauged Wess-Zumino-Witten models. The configuration of strings and fivebranes sourcing this geometry is well-understood, as is the correspondence to states/operators in the dual CFT2. One can analytically continue the construction to Euclidean AdS3 (i.e. the hyperbolic ball ℍ3+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\mathbb{H}}_3^{+} $$\\end{document}) and consider the orbifold by any infinite discrete (Kleinian) group generated by a set of elliptic elements γi ∈ SL(2, ℂ), γiki\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\gamma}_i^{{\ extrm{k}}_i} $$\\end{document} = \U0001d7d9, i = 1, . , K. The resulting geometry consists of multiple conical defects traveling along geodesics in ℍ3+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\mathbb{H}}_3^{+} $$\\end{document}, and provides a semiclassical bulk description of correlation functions in the dual CFT involving the corresponding defect operators, which is nonperturbatively exact in α′. The Lorentzian continuation of these geometries describes a collection of defects colliding to make a BTZ black hole. We comment on a recent proposal to use such correlators to prepare a basis of black hole microstates, and elaborate on a picture of black hole formation and evaporation in terms of the underlying brane dynamics in the bulk.

A Note on Integrability Loss in Fuzzball Geometries

AbstractThe dynamics of certain string configurations in a class of fivebrane supertube backgrounds is studied. In the decoupling limit of the fivebranes, these solutions are known to admit an exact description in worldsheet string theory and string propagation is integrable. For the asymptotically flat solutions, by using analytic tools of classical Hamiltonian systems, the non‐integrability of classical string motion is proved. This suggests that string dynamics in circular supertube geometries exhibit a regime of chaotic behavior.

S-duality in Toverline{T} -deformed CFT

Toverline{T} deformed conformal field theories can be reformulated as worldsheet theories of non-critical strings. We use this correspondence to compute and study the Toverline{T} deformed partition sum of a symmetric product CFT. We find that it takes the form of a partition sum of a second quantized string theory with a worldsheet given by the product of the seed CFT and a gaussian sigma model with the two-torus as target space. We show that deformed symmetric product theory admits a natural UV completion that exhibits a strong weak coupling ℤ2 duality that interchanges the momentum and winding numbers and maps the Toverline{T} -coupling λ to its inverse 1/λ. The ℤ2 duality is part of a full O(2, 2, ℤ)-duality group that includes a PSL(2, ℤ) acting on the complexified Toverline{T} coupling. The duality symmetry eliminates the appearance of complex energies at strong coupling for all seed CFTs with central charge c ≤ 6.

Bi-η and bi-λ deformations of ℤ4 permutation supercosets

Integrable string sigma models on AdS3 backgrounds with 16 supersymmetries have the distinguishing feature that their superisometry group is a direct product. As a result the deformation theory of these models is particularly rich since the two supergroups in the product can be deformed independently. We construct bi-η and bi-λ deformations of two classes of ℤ4 permutation supercoset sigma models, which describe sectors of the Green-Schwarz and pure-spinor string worldsheet theories on type II AdS3 backgrounds with pure R-R flux. We discuss an important limit of these models when one supergroup is undeformed. The associated deformed supergravity background should preserve 8 supersymmetries and is expected to have better properties than the full bi-deformation. As a step towards investigating the quantum properties of these models, we study the two-loop RG flow of the bosonic truncation of the bi-λ deformation.

Target space entanglement entropy

We define a notion of target space entanglement entropy. Rather than partitioning the base space on which the theory is defined, we consider partitions of the target space. This is the physical case of interest for first-quantized theories, such as worldsheet string theory. We associate to each subregion of the target space a suitably chosen subalgebra of observables mathcal{A} . The entanglement entropy is calculated as the entropy of the density matrix restricted to mathcal{A} . As an example, we illustrate our framework by computing spatial entanglement in first-quantized many-body quantum mechanics. The algebra mathcal{A} is chosen to reproduce the entanglement entropy obtained by embedding the state in the fixed particle sub-sector of the second-quantized Hilbert space. We then generalize our construction to the quantum field-theoretical setting.

The discrete Green-Schwarz mechanism in 6D F-theory and elliptic genera of non-critical strings

We study global anomalies of discrete gauge symmetries in six-dimensional supergravities and their realizations in F-theory. We explicitly construct a discrete Green-Schwarz mechanism that depends on the choice of a coupling constant and on a certain quadratic refinement in differential cohomology. By geometrically engineering theories with G = ℤ3 gauge symmetry and no tensor multiplets, we observe that a particular choice of the quadratic refinement is singled out in F-theory. This implies new Swampland constraints on the discrete charge spectra of 6d supergravities. On the other hand, the discrete Green-Schwarz coupling depends on the geometry of the Calabi-Yau. We use anomaly inflow to relate this to a ’t Hooft anomaly of the induced global symmetry in the worldsheet theories of non-critical strings. Using topological symmetry lines, we further relate this anomaly to the modular properties of twisted-twined elliptic genera. We then argue that the latter are encoded in the A-model topological string partition functions on different torus fibrations that are equipped with a flat torsional B-field. This allows us to derive a geometric expression for the global discrete anomaly in terms of the height-pairing of a multi-section on a genus one fibered Calabi-Yau.

Worldsheet computation of heavy-light correlators

We compute a large collection of string worldsheet correlators describing light probes interacting with heavy black hole microstates. The heavy states consist of NS5 branes carrying momentum and/or fundamental string charge. In the fivebrane decoupling limit, worldsheet string theory on a family of such backgrounds is given by exactly solvable null-gauged WZW models. We construct physical vertex operators in these cosets, including all massless fluctuations. We compute a large class of novel heavy-light-light-heavy correlators in the AdS3 limit, where the light operators include those dual to chiral primaries of the holographically dual CFT. We compare a subset of these correlators to the holographic CFT at the symmetric product orbifold point, and find precise agreement in all cases, including for light operators in twisted sectors of the orbifold CFT. The agreement is highly non-trivial, and includes amplitudes that describe the analogue of Hawking radiation for these microstates. We further derive a formula for worldsheet correlators consisting of n light insertions on these backgrounds, and discuss which subset of these correlators are likely to be protected. As a test, we compute a heavy-light five-point function, obtaining precisely the same result both from the worldsheet and the symmetric orbifold CFT. This paper is a companion to and extension of [1].

Baby universes and worldline field theories

The quantum gravity path integral involves a sum over topologies that invites comparisons to worldsheet string theory and to Feynman diagrams of quantum field theory. However, the latter are naturally associated with the non-abelian algebra of quantum fields, while the former has been argued to define an abelian algebra of superselected observables associated with partition-function-like quantities at an asymptotic boundary. We resolve this apparent tension by pointing out a variety of discrete choices that must be made in constructing a Hilbert space from such path integrals, and arguing that the natural choices for quantum gravity differ from those used to construct QFTs. We focus on one-dimensional models of quantum gravity in order to make direct comparisons with worldline QFT. We also restrict attention to models in which worldlines do not split apart or join together.

A defect in AdS3/CFT2 duality

AdS3 string theory in the stringy regime k = (RAdS/ℓs)2< 1 provides a laboratory for the study of holography in which both sides of AdS/CFT duality are under fairly good control. Worldsheet string theory is solvable, and for closed strings the dual spacetime CFT is a deformation of a symmetric product orbifold. Here we extend this construction to include open strings by adding a probe D-string, described semiclassically by an AdS2 D-brane in AdS3. The dual defect or boundary conformal field theory (BCFT) is again a deformed symmetric product, which now describes the Fock space of long open and closed strings near the AdS boundary, with a boundary deformation implementing the open/closed transition in addition to the symmetric product ℤ2 twist deformation that implements closed string joining/splitting. The construction thus provides an explicit example of an AdS3/BCFT2 duality.

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.

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.

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.

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.

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.

Bootstraps to strings: solving random matrix models with positivity

A new approach to solving random matrix models directly in the large N limit is developed. First, a set of numerical values for some low-pt correlation functions is guessed. The large N loop equations are then used to generate values of higher-pt correlation functions based on this guess. Then one tests whether these higher-pt functions are consistent with positivity requirements, e.g., (tr M2k) ≥ 0. If not, the guessed values are systematically ruled out. In this way, one can constrain the correlation functions of random matrices to a tiny subregion which contains (and perhaps converges to) the true solution. This approach is tested on single and multi-matrix models and handily reproduces known solutions. It also produces strong results for multi-matrix models which are not believed to be solvable. A tantalizing possibility is that this method could be used to search for new critical points, or string worldsheet theories.

Very special TJ¯ deformed CFT

We study a very special class of $T\bar{J}$ deformations of conformal field theories in two dimensions. While the deformations break the Lorentz symmetry, they preserve the twisted Lorentz symmetry. The resulting theory has right-moving Virasoro as well as left-moving translation and left-moving (chiral) scale symmetry without left-moving special conformal symmetry (nor left-moving Virasoro symmetry). As in the original $T\bar{J}$ deformations, they may be regarded as an operator dependent non-local change of coordinates. We show concrete examples based on worldsheet string theory and discuss how the non-unitary nature enables us to circumvent various no-go theorems.