World-sheet Model Research Articles

Charting the conformal manifold of holographic CFT$_2$'s

We construct new continuous families of AdS_3× S^3× T^4AdS3×S3×T4 and AdS_3× S^3× S^3× S^1AdS3×S3×S3×S1 solutions in heterotic and type II supergravities. These families are found in three-dimensional consistent truncations and controlled by 17 parameters, which include TsT \betaβ deformations and encompass several supersymmetric sub-families. The different uplifts are constructed in a unified fashion by means of Exceptional Field Theory (ExFT). This allows the computation of the Kaluza-Klein spectra around the deformations, to test the stability of the solutions, and to interpret them holographically and as worldsheet models. To achieve this, we describe how the half-maximal S(8,8)S(8,8) ExFT can be embedded into E_{8(8)}E8(8) ExFT.

Beta deformed sigma model and strong deformation coupling limit

We study the beta deformation of the superstring in AdS5 × S5 at all orders in the deformation parameter, employing the pure spinor formalism. This is necessary in order to study the regime of strong deformation parameter, which in the field side is related to fishnet theories. We compare the pure spinor sigma model approach to the previously known supergravity description. We find a complete agreement. Moreover, the BRST structure of the worldsheet model provides a natural explanation of the peculiar features of the worldsheet model in the fishnet limit. In particular, we study the degeneracy of the sigma model Lagrangian. We show that the BRST structure is responsible for a particularly “tame” degeneration of the fishnet sigma-model.

Massive Strings from a Field Theory with Ghosts.

In this Letter, we present the α^{'}-exact background equations of motion of the bosonic chiral string (also known as Hohm-Siegel-Zwiebach model), with the spin-two ghost fields integrated out. This is the first instance of a world sheet model in which all corrections are fully determined in a generic curved spacetime. As a concrete cross-check, we find complete agreement between all three-point and a sample of four-point tree-level scattering amplitudes computed using field theory methods and the chiral string prescription. These equations of motion provide a field theoretical shortcut to compute world sheet correlators in conventional bosonic strings (with an arbitrary number of massless and mass-level-one states) and outline a new perspective on massive resonances in string theory.

On mixed-flux worldsheet scattering in AdS3/CFT2

Strings on AdS3 × S3 × T4 with mixed Ramond-Ramond and Neveu-Schwarz-Neveu-Schwarz flux are known to be classically integrable. This is a crucial property of this model, which cannot be studied by conventional worldsheet-CFT techniques. Integrability should carry over to the quantum level, and the worldsheet S matrix in the lightcone gauge is known up to the so-called dressing factors. In this work we study the kinematics of mixed-flux theories and consider a relativistic limit of the S matrix whereby we can complete the bootstrap program, including the dressing factors for fundamental particles and bound states. This provides an important test for the dressing factors of the full worldsheet model, and offers new insights on the features of the model when the amount of NSNS flux is low.

A\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{A} $$\\end{document}-theory — A brane world-volume theory with manifest U-duality

In this paper, the A\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{A} $$\\end{document}-theory, an extension of F-theory, is described as a fully U-duality covariant brane theory. This theory has some distinguishing features not known from world-sheet models. In particular, seen as a sigma model, both world-volume and target space coordinates are specific representations of the same group (the U-duality group). The U-duality group in question is an exceptional group (a split form of the Ed series). The structure of this group allows it to encompass both the T-duality group of string theory as well as the general linear symmetry group of M\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{M} $$\\end{document}-theory. A\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{A} $$\\end{document}-theory is defined by the current algebras in Hamiltonian formalism, or by world-volume actions in Lagrangian formalism. The spacetime coordinates are selfdual gauge fields on the world-volume, requiring the Gauß law constraints tying the world-volume to spacetime. Solving the Gauß law constraints/the Virasoro constraints gives the world-volume/spacetime sectioning from A\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{A} $$\\end{document}-theory to T\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{T} $$\\end{document}-theory/M\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{M} $$\\end{document}-theory respectively. The A\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{A} $$\\end{document}-theory Lagrangian admits extended symmetry which has not been observed previously in the literature, where the background fields include both the spacetime and the world-volume gravitational fields. We also constructed the four-point amplitude of A\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{A} $$\\end{document}-theory in the low energy limit. The amplitude is written in a way that the U-duality symmetry is manifest, but after solving the section condition, it reduces to the usual four-graviton amplitude.In the previous papers, we have referred to this model as F-theory, however, F-theory initiated by Vafa is now a big branch of string theory as the study of elliptic fibrations, so we refer to these constructions as generalized models of theory for all dimensions with all duality symmetries as A\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{A} $$\\end{document}-theory.

Dynamics of non-Abelian strings in the theory interpolating from N=2 to N=1 supersymmetric QCD

We study the dynamics of non-Abelian vortex strings supported in ${\mathcal N}=2$ supersymmetric QCD with the U$(N)$ gauge group and $N_f=N$ quark flavors deformed by the mass $\mu$ of the adjoint matter. In the limit of large $\mu$ the bulk four-dimensional theory flows to ${\mathcal N}=1$ supersymmetric QCD. The dynamics of orientational zero modes of the non-Abelian string is described by the world sheet CP$(N-1)$ model. At $\mu=0$ this model has ${\mathcal N}= \left(2,2\right) $ supersymmetry while at large $\mu$ it flows to the non-supersymmetric CP$(N-1)$ model. We solve the world sheet model in the large $N$ approximation and find a rich phase structure with respect to the deformation parameter $\mu$ and quark mass differences. The phases include two strong coupling phases and two Higgs phases. In particular, the Higgs phase at small $\mu$ supports CP$(N-1)$ model kinks representing confined monopoles of the bulk QCD, while in the large-$\mu$ Higgs phase monopoles disappear.

Amplitudes on plane waves from ambitwistor strings

In marked contrast to conventional string theory, ambitwistor strings remain solvable worldsheet theories when coupled to curved background fields. We use this fact to consider the quantization of ambitwistor strings on plane wave metric and plane wave gauge field backgrounds. In each case, the worldsheet model is anomaly free as a consequence of the background satisfying the field equations. We derive vertex operators (in both fixed and descended picture numbers) for gravitons and gluons on these backgrounds from the worldsheet CFT, and study the 3-point functions of these vertex operators on the Riemann sphere. These worldsheet correlation functions reproduce the known results for 3-point scattering amplitudes of gravitons and gluons in gravitational and gauge theoretic plane wave backgrounds, respectively.

Erratum: Large-Nsolution of the heteroticN=(0,2)two-dimensionalCP(N−1)model [Phys. Rev. D77, 125017 (2008)

We continue explorations of non-Abelian strings, focusing on the solution of a heterotic deformation of the CP(N-1) model with an extra right-handed fermion field and N=(0,2) supersymmetry. This model emerges as a low-energy theory on the worldsheet of the BPS-saturated flux tubes (strings) in N=2 supersymmetric QCD deformed by a superpotential of a special type breaking N=2 supersymmetry down to N=1. Using large-N expansion we solve this model to the leading order in 1/N. Our solution exhibits spontaneous supersymmetry breaking for all values of the deformation parameter. We identify the Goldstino field. The discrete Z_{2N} symmetry is shown to be spontaneously broken down to Z_2; therefore, the worldsheet model has N strictly degenerate vacua (with nonvanishing vacuum energy). Thus, the heterotic CP(N-1) model is in the deconfinement phase. We can compare this dynamical pattern, on the one hand, with the N=(2,2) CP(N-1) model which has N degenerate vacua with unbroken supersymmetry, and, on the other hand, with nonsupersymmetric CP(N-1) model with split quasivacua and the Coulomb/confining phase. We determine the mass spectrum of the heterotic CP(N-1) model in the large-N limit.

Conformal current algebra in two dimensions

We construct a non-chiral current algebra in two dimensions consistent with conformal invariance. We show that the conformal current algebra is realized in non-linear sigma-models on supergroup manifolds with vanishing Killing form, with or without a Wess-Zumino term. The current algebra is computed using two distinct methods. First we exploit special algebraic properties of supergroups to compute the exact two- and three-point functions of the currents and from them we infer the current algebra. The algebra is also calculated by using conformal perturbation theory about the Wess-Zumino-Witten point and resumming the perturbation series. We also prove that these models realize a non-chiral Kac-Moody algebra and construct an infinite set of commuting operators that is closed under the action of the Kac-Moody generators. The supergroup models that we consider include models with applications to statistical mechanics, condensed matter and string theory. In particular, our results may help to systematically solve and clarify the quantum integrability of PSU(n|n) models and their cosets, which appear prominently in string worldsheet models on anti-deSitter spaces.

Description of the heterotic string solutions inU(N)supersymmetric QCD

We continue the study of heterotic non-Abelian BPS-saturated flux tubes (strings). Previously, such solutions were obtained [1] in a particular U(2) gauge theory: N=2 supersymmetric QCD deformed by superpotential terms of a special type breaking N=2 supersymmetry down to N=1. Here we generalize the previous results to U(N) gauge theories. As was suggested by Edalati and Tong [2], the string world sheet theory is a heterotic N=(0,2) sigma model, with the CP(N-1) target space for bosonic fields and an extra right-handed fermion which couples to the fermion fields of the N=(2,2) CP(N-1) model. We derive the heterotic N=(0,2) world sheet model directly from the U(N) bulk theory. Parameters of the bulk theory are related to those of the world sheet theory. Qualitatively this relation turns out to be the same as in the U(2) case.

Erratum: Heterotic flux tubes inN=2supersymmetric QCD withN=1preserving deformations [Phys. Rev. D77, 125016 (2008)

We consider non-Abelian BPS-saturated flux tubes (strings) in N=2 supersymmetric QCD deformed by superpotential terms of a special type breaking N=2 supersymmetry down to N=1. Previously it was believed that worldsheet supersymmetry is "accidentally" enhanced due to the facts that N =(1,1) SUSY is automatically elevated up to N=(2,2) on CP(N-1) and, at the same time, there are no N=(0,2) generalizations of the bosonic CP(N-1) model. Edalati and Tong noted that the target space is in fact CP(N-1) x C rather than CP(N-1). This allowed them to suggest a "heterotic" N=(0,2) sigma model, with the CP(N-1) target space for bosonic fields and an extra right-handed fermion which couples to the fermion fields of the N=(2,2) CP(N-1) model. We derive the heterotic N=(0,2) worldsheet model directly from the bulk theory. The relation between the bulk and worldsheet deformation parameters we obtain does not coincide with that suggested by Edalati and Tong at large values of the deformation parameter. For polynomial deformation superpotentials in the bulk we find nonpolynomial response in the worldsheet model. We find a geometric representation for the heterotic model. Supersymmetry is proven to be spontaneously broken for small deformations (at the quantum level). This confirms Tong's conjecture. A proof valid for large deformations will be presented in the subsequent publication.

Worldsheet theories for non-geometric string backgrounds

We show that twisted doubled tori can be used to construct a general class of worldsheet models describing non-geometric string backgrounds. By employing a first order formulation of interacting chiral bosons, we first refine the analysis on the general conditions of worldsheet Lorentz invariance and then prove that twisted doubled tori provide good duality symmetric backgrounds. Subsequently we apply our general analysis to several examples which enable us to gain new insight on the difference between geometric, locally geometric and genuine non-geometric backgrounds.

Heterotic AdS3/ CFT2 duality with [formula omitted] spacetime supersymmetry

We discuss the AdS 3/ CFT 2 duality of a heterotic three-charge model with ( 0 , 4 ) target space supersymmetry. The worldsheet theory for heterotic strings on the AdS 3 × S 3 / Z N × T 4 near-horizon geometry was constructed by Kutasov et al. [D. Kutasov, F. Larsen, R.G. Leigh, String theory in magnetic monopole backgrounds, Nucl. Phys. B 550 (1999) 183, hep-th/9812027]. We propose that the dual conformal field theory is given by a two-dimensional ( 0 , 4 ) sigma model arising on the Higgs branch of an orbifolded ADHM model. As a non-trivial consistency check of the correspondence, we find that the left- and right-moving central charges of the infrared conformal field theory agree with those predicted by the worldsheet model. Moreover, using the entropy function formalism, we show that to next-to-leading order the central charge can also be obtained from an α ′ -corrected supergravity theory.

Heterotic flux tubes inN=2supersymmetric QCD withN=1preserving deformations

We consider non-Abelian Bogomol'nyi-Prasad-Sommerfield-saturated flux tubes (strings) in $\mathcal{N}=2$ supersymmetric QCD deformed by superpotential terms of a special type breaking $\mathcal{N}=2$ supersymmetry down to $\mathcal{N}=1$. Previously it was believed that world sheet supersymmetry is accidentally enhanced due to the facts that $\mathcal{N}=(1,1)$ supersymmetry is automatically elevated up to $\mathcal{N}=(2,2)$ on $CP(N\ensuremath{-}1)$ and, at the same time, there are no $\mathcal{N}=(0,2)$ generalizations of the bosonic $CP(N\ensuremath{-}1)$ model. Edalati and Tong noted that the target space is in fact $CP(N\ensuremath{-}1)\ifmmode\times\else\texttimes\fi{}C$ rather than $CP(N\ensuremath{-}1)$. This allowed them to suggest a heterotic $\mathcal{N}=(0,2)$ sigma model, with the $CP(N\ensuremath{-}1)$ target space for bosonic fields and an extra right-handed fermion which couples to the fermion fields of the $\mathcal{N}=(2,2)$ $CP(N\ensuremath{-}1)$ model. We derive the heterotic $\mathcal{N}=(0,2)$ world sheet model directly from the bulk theory. The relation between the bulk and world sheet deformation parameters we obtain does not coincide with that suggested by Edalati and Tong at large values of the deformation parameter. For polynomial deformation superpotentials in the bulk we find nonpolynomial response in the world sheet model. We find a geometric representation for the heterotic model. Supersymmetry is proven to be spontaneously broken for small deformations (at the quantum level). This confirms Tong's conjecture. A proof valid for large deformations will be presented in the subsequent publication.

Large-Nsolution of the heteroticN=(0,2)two-dimensionalCP(N−1)model

We continue explorations of non-Abelian strings, focusing on the solution of a heterotic deformation of the $CP(N\ensuremath{-}1)$ model with an extra right-handed fermion field and $\mathcal{N}=(0,2)$ supersymmetry. This model emerges as a low-energy theory on the world sheet of the Bogomol'nyi-Prasad-Sommerfield-saturated flux tubes (strings) in $\mathcal{N}=2$ supersymmetric QCD deformed by a superpotential of a special type breaking $\mathcal{N}=2$ supersymmetry down to $\mathcal{N}=1$. Using large-$N$ expansion we solve this model to the leading order in $1/N$. Our solution exhibits spontaneous supersymmetry breaking for all values of the deformation parameter. We identify the Goldstino field. The discrete ${Z}_{2N}$ symmetry is shown to be spontaneously broken down to ${Z}_{2}$; therefore the world sheet model has $N$ strictly degenerate vacua (with nonvanishing vacuum energy). Thus, the heterotic $CP(N\ensuremath{-}1)$ model is in the deconfinement phase. We can compare this dynamical pattern, on the one hand, with the $\mathcal{N}=(2,2)$ $CP(N\ensuremath{-}1)$ model which has $N$ degenerate vacua with unbroken supersymmetry, and, on the other hand, with the nonsupersymmetric $CP(N\ensuremath{-}1)$ model with split quasivacua and the Coulomb/confining phase. We determine the mass spectrum of the heterotic $CP(N\ensuremath{-}1)$ model in the large-$N$ limit.

Towards a string bit formulation of Script N = 4 super Yang-Mills

We show that planar cal N=4 Yang-Mills theory at zero 't Hooft coupling can be efficiently described in terms of 8 bosonic and 8 fermionic oscillators. We show that these oscillators can serve as world-sheet variables, the string bits, of a discretized string. There is a one to one correspondence between the on shell gauge invariant words of the free Y-M theory and the states in the oscillators' Hilbert space, obeying a local gauge and cyclicity constraints. The planar two-point functions and the three-point functions of all gauge invariant words are obtained by the simple delta-function overlap of the corresponding discrete string world sheet. At first order in the 't Hooft coupling, i.e. at one-loop in the Y-M theory, the logarithmic corrections of the planar two-point and the three-point functions can be incorporated by nearest neighbour interactions among the discretized string bits. In the SU(2) sub-sector we show that the one-loop corrections to the structure constants can be uniquely determined by the symmetries of the bit picture. For the SU(2) sub-sector we construct a gauged, linear, discrete world-sheet model for the oscillators, with only nearest neighbour couplings, which reproduces the anomalous dimension Hamiltonian up to two loops. This model also obeys BMN scaling to all loops.

On minisuperspace models of S-branes

In this note we reconsider the minisuperspace toy models for rolling and bouncing tachyons. We show that the theories require to choose boundary conditions at infinity since particles in an exponentially unbounded potential fall to infinity in finite world-sheet time. Using standard techniques from operator theory, we determine the possible boundary conditions and we compute the corresponding energy spectra and minisuperspace 3-point functions. Based on this analysis we argue in particular that world-sheet models of S-branes possess a discrete spectrum of conformal weights containing both positive and negative values. Finally, some suggestions are made for possible relations with previous studies of the minisuperspace theory.

A mean field approximation to the worldsheet model of planar φ3 field theory

We develop an approximation scheme for our worldsheet model of the sum of planar diagrams based on mean field theory. At finite coupling the mean field equations show a weak coupling solution that resembles the perturbative diagrams and a strong coupling solution that seems to represent a tensionless soup of field quanta. With a certain amount of fine-tuning, we find a solution of the mean field equations that seems to support string formation.

Time-dependent backgrounds in supergravity and string theory

Time-dependent solutions of supergravity and string theory are studied. The examples are obtained from de Sitter deformation of gauge/gravity dualities, analytical continuation of static solutions, and ``exactly solvable'' worldsheet models. Among other things, it is shown that turning on a Hubble parameter in the background of a confining gauge theory in four dimensions can restore chiral symmetry. Some of the solutions obtained from analytical continuation have the interpretation of a universe with a bounce separating a big bang from a big crunch singularity. In the worldsheet context, it is argued why string propagation close to a Milne-type cosmological singularity might be physically non-singular.

Linear Sigma Models for Open Strings

We formulate and study a class of massive N=2 supersymmetric gauge field theories coupled to boundary degrees of freedom on the strip. For some values of the parameters, the infrared limits of these theories can be interpreted as open string sigma models describing D-branes in large-radius Calabi-Yau compactifications. For other values of the parameters, these theories flow to CFTs describing branes in more exotic, non-geometric phases of the Calabi-Yau moduli space such as the Landau-Ginzburg orbifold phase. Some simple properties of the branes (like large radius monodromies and spectra of worldvolume excitations) can be computed in our model. We also provide simple worldsheet models of the transitions which occur at loci of marginal stability, and of Higgs-Coulomb transitions.