World-sheet Supersymmetry Research Articles

Nonrelativistic expansion of Green-Schwarz strings on AdS5 × S5

We perform nonrelativistic expansions of type IIB AdS5×S5 Green-Schwarz (GS) superstrings upto quadratic order in fermionic excitation. We carry out a systematic 1/c expansion both for the bosonic as well as the fermionic sector of the type IIB model and explore the LO theory in detail. We explore various global as well as local symmetries of the nonrelativistic sigma model at LO including the world-sheet supersymmetry. As a special case, we choose the flat gauge and explore the longitudinal T-duality rules for the LO theory. Finally, we comment on the NLO theory and discuss some of its interesting properties including the scale invariance.

D=5 holomorphic Chern-Simons and the pure spinor superstring

The physical states of D=5 holomorphic Chern-Simons theory correspond to on-shell D=10 open superstring states in the cohomology of q+, where q+ is one of the 16 spacetime supersymmetry generators. Scattering amplitudes of these states can be computed either using the usual Ramond-Neveu-Schwarz (RNS) superstring prescription with N=1 worldsheet supersymmetry, or using a topological ĉ=5 string theory with twisted N=2 worldsheet supersymmetry.It will be argued that the relation between D=5 holomophic Chern-Simons and the RNS superstring is identical to the relation between the pure spinor superstring and the recently constructed B-RNS-GSS superstring which has both N=1 worldsheet supersymmetry and D=10 spacetime supersymmetry. Physical states of the pure spinor superstring correspond to on-shell B-RNS-GSS states which are in the cohomology of λαqα, where λα is a D=10 pure spinor. And scattering amplitudes of these states can be computed either using the full B-RNS-GSS superstring prescription with N=1 worldsheet supersymmetry, or using the pure spinor superstring amplitude prescription with twisted N=2 worldsheet supersymmetry. This should be useful for proving equivalence of the RNS and pure spinor amplitude prescriptions and for clarifying the relation of their multiloop subtleties.

The fate of discrete torsion on resolved heterotic [formula omitted] orbifolds using (0,2) GLSMs

This paper aims to shed light on what becomes of discrete torsion within heterotic orbifolds when they are resolved to smooth geometries. Gauged Linear Sigma Models (GLSMs) possessing (0,2) worldsheet supersymmetry are employed as interpolations between them. This question is addressed for resolutions of the non–compact C3/Z2×Z2 and the compact T6/Z2×Z2 orbifolds to keep track of local and global aspects. The GLSMs associated with the non–compact orbifold with or without torsion are to a large extent equivalent: only when expressed in the same superfield basis, a field redefinition anomaly arises among them, which in the orbifold limit reproduces the discrete torsion phases. Previously unknown, novel resolution GLSMs for T6/Z2×Z2 are constructed. The GLSM associated with the torsional compact orbifold suffers from mixed gauge anomalies, which need to be cancelled by appropriate logarithmic superfield dependent FI–terms on the worldsheet, signalling H–flux due to NS5–branes supported at the exceptional cycles.

Towards non-Archimedean superstrings

An action for a prospect of a p-adic open superstring on a target Minkowski space is proposed. The action is constructed for ‘worldsheet’ fields taking values in the p-adic field Qp, but it is assumed to be obtained from a discrete action on the Bruhat-Tits tree. This action is proven to have an analogue of worldsheet supersymmetry and the superspace action is also constructed in terms of superfields. The action does not have conformal symmetry, however it is implemented in the definition of the amplitudes. The tree-level amplitudes for this theory are obtained for N vertex operators corresponding to tachyon superfields and a Koba-Nielsen formula is obtained. Finally, four-point amplitudes are computed explicitly and they are compared to previous work on p-adic superstring amplitudes.

Celestial OPEs and w1+\u221e algebra from worldsheet in string theory

Celestial operator product expansions (OPEs) arise from the collinear limit of scattering amplitudes and play a vital role in celestial holography. In this paper, we derive the celestial OPEs of massless fields in string theory from the worldsheet. By studying the worldsheet OPEs of vertex operators in worldsheet CFT and further examining their behaviors in the collinear limit, we find that new vertex operators for the massless fields in string theory are generated and become dominant in the collinear limit. Mellin transforming to the conformal basis yields exactly the celestial OPEs in celestial CFT. We also derive the celestial OPEs from the collinear factorization of string amplitudes and the results derived in these two different methods are in perfect agreement with each other. Our final formulae of celestial OPEs are applicable to general dimensions, corresponding to Einstein-Yang-Mills theory supplemented by some possible higher derivative interactions. Specializing to 4D, we reproduce all the celestial OPEs for gluon and graviton in the literature. We consider various string theories, including the open and closed bosonic string, as well as the closed superstring theory with mathcal{N} = 1 and mathcal{N} = 2 worldsheet supersymmetry. In the case of mathcal{N} = 2 string, we also derive all the overline{mathrm{SL}left(2,mathbb{R}right)} descendant contributions in the celestial OPE; the soft sector of such OPE just yields the w1+∞ algebra after rewriting in terms of chiral modes. Our stringy derivation of celestial OPEs thus initiates the first step towards the microscopic realization of celestial CFT dual to string theory in flat spacetime.

Untwisting the pure spinor formalism to the RNS and twistor string in a flat and AdS5 × S 5 background

The pure spinor formalism for the superstring can be formulated as a twisted N=2 worldsheet theory with fermionic generators $j_{BRST}$ and composite $b$ ghost. After untwisting the formalism to an N=1 worldsheet theory with fermionic stress tensor $j_{BRST}+b$, the worldsheet variables combine into N=1 worldsheet superfields $X^m$ and $\Theta^\alpha$ together with a superfield constraint relating $DX^m$ and $D\Theta^\alpha$. The constraint implies that the worldsheet superpartner of $\theta^\alpha$ is a bosonic twistor variable, and different solutions of the constraint give rise to the pure spinor or extended RNS formalisms, as well as a new twistor-string formalism with manifest N=1 worldsheet supersymmetry. These N=1 worldsheet methods generalize in curved Ramond-Ramond backgrounds, and a manifestly N=1 worldsheet supersymmetric action is proposed for the superstring in an $AdS_5\times S^5$ background in terms of the twistor superfields. This $AdS_5\times S^5$ worldsheet action is a remarkably simple fermionic coset model with manifest $PSU(2,2|4)$ symmetry and might be useful for computing $AdS_5\times S^5$ superstring scattering amplitudes.

F-Theory, spinning black holes and multi-string branches

We study 5d supersymmetric black holes which descend from strings of generic $\mathcal{N}=(1,0)$ supergravity in 6d. These strings have an F-theory realization in 6d as D3 branes wrapping smooth genus $g$ curves in the base of elliptic 3-folds. They enjoy $(0,4)$ worldsheet supersymmetry with an extra $SU(2)_L$ current algebra at level $g$ realized on the left-movers. When the smooth curves degenerate they lead to multi-string branches and we find that the microscopic worldsheet theory flows in the IR to disconnected 2d CFTs having different central charges. The single string sector is the one with maximal central charge, which when wrapped on a circle, leads to a 5d spinning BPS black hole whose horizon volume agrees with the leading entropy prediction from the Cardy formula. However, we find new phenomena where this branch meets other branches of the CFT. These include multi-string configurations which have no bound states in 6 dimensions but are bound through KK momenta when wrapping a circle, as well as loci where the curves degenerate to spheres. These loci lead to black hole configurations which can have total angular momentum relative to a Taub-Nut center satisfying $J^2 > M^3$ and whose number of states, though exponentially large, grows much slower than those of the large spinning black hole.

String corrected spacetimes and [formula omitted]-structure manifolds

Using an effective field theory approach and the language of SU(N)-structures, we study higher derivative corrections to the supersymmetry constraints for compactifications of string or M-theory to Minkowski space. Our analysis is done entirely in the target space and is thus very general, and does not rely on theory-dependent details such as the amount of worldsheet supersymmetry. For manifolds of real dimension n<4 we show that internal geometry remains flat and uncorrected. For n=4,6, Kähler manifolds with SU(N)-holonomy can become corrected to SU(N)-structure, while preserving supersymmetry, once corrections are included.

Delta-function interactions for the bosonic and spinning strings and the generation of Abelian gauge theory

We construct contact interactions for bosonic and spinning strings. In the tensionless limit of the spinning string this reproduces the super-Wilson loop that couples spinor matter to Abelian gauge theory. Adding boundary terms that quantise the motion of charges results in a string model equivalent to spinor QED. The strings represent lines of electric flux connected to the charges. The purely bosonic model is spoilt by divergences that are excluded from the spinning model by world-sheet supersymmetry, indicating a preference for spinor matter.

Supersymmetric closed string tachyon cosmology: a first approach

We give a worldline supersymmetric formulation for the effective action of closed string tachyon in a FRW background. This is done considering that, as shown by Vafa, the effective theory of closed string tachyons can have worldsheet supersymmetry. The Hamiltonian is constructed by means of the Dirac procedure and written in a quantum version. By using the supersymmetry algebra we are able to find solutions to the Wheeler-DeWitt equation via a more simple set of first order differential equations.

World-sheet stability, space-time horizons and cosmic censorship

Previously, we have analyzed the stability and supersymmetry of the heterotic superstring world sheet in the background Friedmann space-time generated by a perfect fluid with energy density ρ and pressure p = (γ − 1) ρ. The world sheet is tachyon-free within the range 2/3 ≤ γ ≤ ∞, and globally supersymmetric in the Minkowski-space limit ρ = ∞, or when γ = 2/3, which is the equation of state for stringy matter and corresponds to the Milne universe, that expands along its apparent horizon. Here, this result is discussed in greater detail, particularly with regard to the question of horizon structure, cosmic censorship, the TCP theorem, and local world-sheet supersymmetry. Also, we consider the symmetric background space-time generated by a static, electrically (or magnetically) charged matter distribution of total mass \(\mathcal{M}\) and charge Q, and containing a radially directed macroscopic string. We find that the effective string mass m satisfies the inequality m2 ≥ 0, signifying stability, provided that \(\mathcal{M}^2 \geqslant Q^2\), which corresponds to the Reissner-Nordstrom black hole. The case of marginal string stability, m2 = 0, is the extremal solution \(\mathcal{M}^2 = Q^2\), which was shown by Gibbons and Hull to be supersymmetric, and has a marginal horizon. If \(\mathcal{M}^2 < Q^2\), the horizon disappears, m2 < 0, and the string becomes unstable.

Higher poles and crossing phenomena from twisted genera

We demonstrate that Appell-Lerch sums with higher order poles as well as their modular covariant completions arise as partition functions in the cigar conformal field theory with worldsheet supersymmetry. The modular covariant derivatives of the elliptic genus of the cigar give rise to operator insertions corresponding to (powers of) right-moving momentum, left-moving fermion number, as well as a term corresponding to an ordinary zero mode partition sum. To show this, we demonstrate how the right-moving supersymmetric quantum mechanics (and in particular the Hamiltonian and spectral density) depend on the imaginary part of the chemical potential for angular momentum. As a consequence of our analysis we find that varying the imaginary part of the chemical potential for angular momentum on the cigar gives rise to a wall-crossing phenomenon in the bound state contribution to the elliptic genus, while the full elliptic genus is a continuous function of the chemical potential.

Closed string partition functions in toroidal compactifications of doubled geometries

We revisit partition functions of closed strings on toroidal backgrounds, including their $\mathbb{Z}_N$ shift orbifolds in the formalism where the dimension of the target space is doubled to make T-duality manifest. In such a T-duality covariant formalism, the constraint equation imposes a form of chiral factorization. Our computation furnishes a non-trivial consistency check for the quantum worldsheet theory of the doubled sigma model, when strings are placed on general toroidal backgrounds. The topological term that mixes the physical space and its T-dual is crucial in demonstrating that chiral factorization works, and that we obtain the correct partition function after imposing the constraints. Finally, we discuss how our results extend to $\mathcal{N}=1$ worldsheet supersymmetry and string worldsheets of higher genus.

Worldsheet two- and four-point functions at one loop in AdS3/CFT2

In this note we study worldsheet two- and four-point functions at the one-loop level for the type IIA superstring in AdS3×S3×M4. We first address the regularization ambiguity that appears in the dispersion relation derived from integrability. We demonstrate that only the regulator treating all fields equally respects worldsheet supersymmetry. This is done in an implicit regularization scheme where all divergent terms are collected into master tadpole-type integrals. We then investigate one-loop two-body scattering on the string worldsheet and verify that a recent proposal for the dressing phase reproduces explicit worldsheet computations. All calculations are done in a near-BMN like expansion of the Green–Schwarz superstring equipped with quartic fermions.

Twining genera of (0,4) supersymmetric sigma models on K3

Conformal field theories with (0,4) worldsheet supersymmetry and K3 target can be used to compactify the E8xE8 heterotic string to six dimensions in a supersymmetric manner. The data specifying such a model includes an appropriate configuration of 24 gauge instantons in the E8xE8 gauge group to satisfy the constraints of anomaly cancellation. In this note, we compute twining genera - elliptic genera with appropriate insertions of discrete symmetry generators in the trace - for (0,4) theories with various instanton embeddings. We do this by constructing linear sigma models which flow to the desired conformal field theories, and using the techniques of localization. We present several examples of such twining genera which are consistent with a moonshine relating these (0,4) models to the finite simple sporadic group M24.

Tachyon potentials from a supersymmetric FRW model

Considering that the effective theory of closed string tachyons can have worldsheet supersymmetry, as shown by Vafa, we study a worldline supersymmetric action in a FRW background, whose superpotential originates a tachyon scalar potential. There are such potentials with spontaneously broken supersymmetry at the instability and supersymmetric after tachyon condensation. Furthermore, given a tachyonic potential, the superpotential can be computed by a power series ansatz and has a free parameter which can be chosen such that complex solutions become real.

Spectra of coset sigma models

We compute the complete 1-loop spectrum of anomalous dimensions for the bulk fields of non-linear sigma models on symmetric coset (super)spaces G/H, both with and without world-sheet supersymmetry. In addition, we provide two new methods for the construction of partition functions in the infinite radius limit and demonstrate their efficiency in the case of (super)sphere sigma models. Our results apply to a large number of target spaces including superspheres and superprojective spaces such as the N=2 sigma model on CP3|4.

Classical and quantum integrability in AdS 2/CFT 1

We investigate the type IIA string on AdS(2)xS(2)xT(6) supported by RR-flux which describes the gravitational side of the AdS(2)/CFT(1) correspondence. While the four-dimensional part AdS(2)xS(2) can be realized as a supercoset, the full superstring has both coset and non-coset excitations, the latter giving rise to massless worldsheet modes, a somewhat novel feature in AdS/CFT. The string is nevertheless known to be integrable at the classical level. In this paper we perform several computations checking aspects of both classical and quantum string integrability. At the classical level we compute energies for the near BMN string and successfully match these against Bethe ansatz predictions. Furthermore, integrability dictates a magnon dispersion relation which we compare with the poles of loop corrected propagators, at both the one and two-loop level. At one loop, where only tadpole diagrams contribute, we find that the bosonic and fermionic contributions sum up to zero. Under the assumption of worldsheet supersymmetry, we then compute the two-loop sunset diagram in the near flat space limit. As in AdS(5)xS(5) we find that the result fits nicely into the sine-square structure of the dispersion relation.

Worldsheet Supersymmetry in Pohlmeyer-Reduced Superstrings

We show that the AdS3 × S3 and AdS5 × S5 superstring theories in the Pohlmeyer-reduced form reveal hidden \U0001d4a9 = (4, 4) and \U0001d4a9 = (8, 8) worldsheet supersymmetries. The characteristic feature of these transformations is the presence of non-local terms.

HIDDEN SUPERSYMMETRY IN POHLMEYER-REDUCED FORM OF AdSn × Sn SUPERSTRINGS

We review how the AdS2 × S2, AdS3 × S3 and AdS5 × S5 superstring theories in the Pohlmeyer-reduced form exhibit hidden [Formula: see text], [Formula: see text] and [Formula: see text] worldsheet supersymmetries, with emphasis on the last two cases. Their characteristic feature is the presence of non-local terms in the supersymmetry transformations.