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 x S^3/Z_N x T^4 near-horizon geometry was constructed by Kutasov, Larsen and Leigh in [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 alpha'-corrected supergravity theory.
We analyse the BRST cohomology of the Ramond sector of heterotic ambitwistor theory. We also write the free string field theory action and compute the supersymmetry transformations.
We show that the formal alpha' expansion for heterotic flux vacua is only sensible when flux quantization and the appearance of string scale cycles in the geometry are carefully taken into account. We summarize a number of properties of solutions with N=1 and N=2 space-time supersymmetry.
Using finite abelian automorphism groups of $K3$ we construct orbifold candidates for Type IIA-heterotic dual pairs with maximal supersymmetry in six and lower dimensions. On the heterotic side, these results extend the series of known reduced rank theories with maximal supersymmetry. The corresponding Type IIA theories generalize the Schwarz and Sen proposal for the dual of the simplest of the reduced rank theories constructed as a novel Type IIA $\IZ_2$ orbifold.
We study the non-linear sigma model realization of a heterotic vacuum with N=2 space-time supersymmetry. We examine the requirements of (0,2) + (0,4) world-sheet supersymmetry and show that a geometric vacuum must be described by a principal two-torus bundle over a K3 manifold.
We obtain a family of heterotic supergravity backgrounds describing non-Kahler warped conifolds with three-form flux and an Abelian gauge bundle, preserving N=1 supersymmetry in four dimensions. At large distance from the singularity the usual Ricci-flat conifold is recovered. By performing a Z_2 orbifold of the T^{1,1} base, the conifold singularity can be blown-up to a four-cycle, leading to a completely smooth geometry. Remarkably, the throat regions of the solutions, which can be isolated from the asymptotic Ricci-flat geometry using a double-scaling limit, possess a worldsheet CFT descrip…
The supersymmetry of near-horizon geometries in heterotic supergravity is considered. A necessary and sufficient condition for a solution to preserve more than the minimal N=2 supersymmetry is obtained. A supersymmetric near-horizon solution is constructed which is a U(1) fibration of AdS3 over a particular Aloff-Wallach space. It is proven that this solution preserves the conditions required for N=2 supersymmetry, but does not satisfy the necessary condition required for further supersymmetry enhancement. Hence, there exist supersymmetric near-horizon heterotic solutions preserving exactly N=…
We analyze the possible dynamical emergence of IR conformal field theory describing the low-energy excitations of near-extremal black holes in five-dimensional compactification of heterotic strings. We find that, by tuning the mass and charges in such a way that the extremal black holes have a classically vanishing horizon area, the near-horizon develops an AdS3 throat and when we combine the low-energy limit with vanishing Newton coupling constant, the system has a dual conformal field theory description. We compare our results with c-extremization and the Kerr/CFT predictions.
We study the constraints of spacetime supersymmetry for perturbative three- and two-dimensional Minkowski vacua of the critical heterotic string. Assuming a standard RNS construction of the spacetime supersymmetry generators and a compact unitary internal superconformal worldsheet theory, we describe the worldsheet structures associated to various spacetime supersymmetries. In three dimensions we show that there are no CFT surprises: each allowed spacetime supersymmetry is realized by a supergravity compactification. As a recent orbifold construction shows, in two dimensions there are more exo…
In this paper we consider compactifications of heterotic strings in the presence of background flux. The background metric is a T^2 fibration over a K3 base times four-dimensional Minkowski space. Depending on the choice of three-form flux different amounts of supersymmetry are preserved (N=2,1,0). For supersymmetric solutions unbroken space-time supersymmetry determines all background fields except one scalar function which is related to the dilaton. The heterotic Bianchi identity gives rise to a differential equation for the dilaton which we discuss in detail for solutions preserving an N=2 …
We use simple current techniques and their relation to orbifolds with discrete torsion for studying the (0,2) CFT/geometry duality with non-rational internal N=2 SCFTs. Explicit formulas for the charged spectra of heterotic SO(10) GUT models are computed in terms of their extended Poincaré polynomials and the complementary Poincaré polynomial which can be computed in terms of the elliptic genera. While non-BPS states contribute to the charged spectrum, their contributions can be determined also for non-rational cases. For model building, with generalizations to SU(5) and SM gauge groups, one c…
D-instanton effects are studied for the IIB orientifold T^2/IΩ(-1)^{F_L} of Sen using type I/heterotic duality. An exact one loop threshold calculation of t_8 \tr F^4 and t_8(\tr F^2)^2 terms for the heterotic string on T^2 with Wilson lines breaking SO(32) to SO(8)^4 is related to D-instanton induced terms in the worldvolume of D7 branes in the orientifold. Introducing D3 branes and using the AdS/CFT correspondence in this case, these terms are used to calculate Yang-Mills instanton contributions to four point functions of the large N_c limit of N=2 USp(2N_c) SYM with four fundamental and one…
We study one-loop quantum corrections to gauge couplings in heterotic vacua with spontaneous supersymmetry breaking. Although in non-supersymmetric constructions these corrections are not protected and are typically model dependent, we show how a universal behaviour of threshold differences, typical of supersymmetric vacua, may still persist. We formulate specific conditions on the way supersymmetry should be broken for this to occur. Our analysis implies a generalised notion of threshold universality even in the case of unbroken supersymmetry, whenever extra charged massless states appear at …
We propose a new formulation of the $D=3$ type II superstring which is manifestly invariant under both target-space $N=2$ supersymmetry and worldsheet $N=(1,1)$ super reparametrizations. This gives rise to a set of twistor (commuting spinor) variables, which provide a solution to the two Virasoro constraints. The worldsheet supergravity fields are shown to play the rôle of auxiliary fields.
We study supersymmetry conditions for the heterotic pure superstring preserving and N=1 supersymmetry in four dimensions directly from the curved superspace defined by the Berkovits-Howe constraints.
Theory Center, Institute of Particle and Nuclear Studies, KEK（高能加速器研究机构粒子与核物理研究本部理论中心）；SOKENDAI (The Graduate University for Advanced Studies)（综合研究大学院大学）
Higher-derivative interactions and transformation rules of the fields in the effective field theories of the massless string states are strongly constrained by space-time symmetries and dualities. Here we use an exact formulation of ten dimensional ${\cal N}=1$ supergravity coupled to Yang-Mills with manifest T-duality symmetry to construct the first order $α'$-corrections of the heterotic string effective action. The theory contains a supersymmetric and T-duality covariant generalization of the Green-Schwarz mechanism that determines the modifications to the leading order supersymmetry transf…
We reconsider the issue of embedding space-time fermions into the four-dimensional N=2 world-sheet supersymmetric string. A new heterotic theory is constructed, taking the right-movers from the N=4 topological extension of the conventional N=2 string but a c=0 conformal field theory supporting target-space supersymmetry for the left-moving sector. The global bosonic symmetry of the full formalism proves to be U(1,1), just as in the usual N=2 string. Quantization reveals a spectrum of only two physical states, one boson and one fermion, which fall in a multiplet of (1,0) supersymmetry.
One of the goals of the landscape program in string theory is to extract information about the space of string vacua in the form of statistical correlations between phenomenological features that are otherwise uncorrelated in field theory. Such correlations would thus represent predictions of string theory that hold independently of a vacuum-selection principle. In this paper, we study statistical correlations between two features which are likely to be central to any potential description of nature at high energy scales: gauge symmetries and spacetime supersymmetry. We analyze correlations be…
We showed that there is no SU(2) Witten anomaly in a large class of 4d N = 2 supersymmetric Heterotic string compactifications. The consistency conditions we consider are the modularity of the new supersymmetric index, the integrality of BPS indices, and the discrete Peccei-Quinn shift symmetries. We also found an example where these conditions are not sufficient to show that the theory is anomaly free. This suggests that there are more conditions in the worldsheet SCFT essential for consistent string compactifications.
We consider heterotic string theory on Eguchi-Hanson space, as a local model of a resolved A_1 singularity in a six-dimensional flux compactification, with an Abelian gauge bundle turned on and non-zero torsion. We show that in a suitable double scaling limit, that isolates the physics near the non-vanishing two-cycle, a worldsheet conformal field theory description can be found. It contains a heterotic coset whose target space is conformal to Eguchi-Hanson. Starting from the blow-down limit of the singularity, it can be viewed as a dynamical deformation of the near-horizon fivebrane backgroun…
We explicitly describe, in the language of four-dimensional N=1 supersymmetric field theory, what happens when the moduli of a heterotic Calabi-Yau compactification change so as to make the internal non-Abelian gauge fields non-supersymmetric. At the edge of the region in Kahler moduli space where supersymmetry can be preserved, an additional anomalous U(1) gauge symmetry appears in the four-dimensional theory. The D-term contribution to the scalar potential associated to this U(1) attempts to force the system back into a supersymmetric configuration and provides a consistent low-energy descri…
Perturbative heterotic string theory develops a single complex tachyonic mode beyond the Hagedorn temperature. We calculate the quartic effective potential for this tachyonic mode at the critical temperature. Equivalently, we determine the quartic effective potential for strong supersymmetric breaking via anti-perdiodic boundary conditions for fermions on a small circle. We give many details of the heterotic tachyon scattering amplitudes, including a unitarity check to fix all normalization constants. We discuss difficulties in obtaining an effective action valid at all radii. We argue that in…
We consider heterotic strings on a warped Eguchi-Hanson space with five-brane and line bundle gauge fluxes. The heterotic string admits an exact CFT description in terms of an asymmetrically gauged SU(2)xSL(2,R) WZW model, in a specific double scaling limit in which the blow-up radius and the string scale are sent to zero simultaneously. This allows us to compute the perturbative 6D spectra for these models in two independent fashions: i) Within the supergravity approximation we employ a representation dependent index; ii) In the double scaling limit we determine all marginal vertex operators …
We investigate the recently proposed Kerr/CFT correspondence in the context of heterotic string theory. The Kerr/CFT correspondence states that the near-horizon states of an extremal four (or higher) dimensional black hole could be identified with a certain chiral conformal field theory under the conjecture that the central charges from the non-gravitational fields vanish. The corresponding Virasoro algebra is generated by a class of diffeomorphisms which preserves the appropriate boundary conditions on the near-horizon geometry. To understand the chiral conformal field theory, we consider the…
In this talk new formulations of the Green--Schwarz heterotic strings in $D$ dimensions that involve commuting spinors, are reviewed. These models are invariant under $n$--extended, world sheet supersymmetry as well as under $N=1$, target space supersymmetry where $n\leq D-2$ and $D=3,4,6,10$. The world sheet supersymmetry replaces $n$ components (and provides a geometrical meaning) of the $κ$--symmetry in the Green--Schwarz approach. The models in $D=10$ for $n=1,2,8$ are discussed explicitly.
We show that the heterotic supersymmetry (Killing spinor equations) and the anomaly cancellation imply the heterotic equations of motion in dimensions five, six, seven, eight if and only if the connection on the tangent bundle is an instanton. For heterotic compactifications in dimension six this reduces the choice of that connection to the unique SU(3) instanton on a manifold with stable tangent bundle of degree zero.
We classify non-nilpotent complex structures on 6-nilmanifolds and their associated invariant balanced metrics. As an application we find a large family of solutions of the heterotic supersymmetry equations with non-zero flux, non-flat instanton and constant dilaton satisfying the anomaly cancellation condition with respect to the Chern connection.
This thesis is the discussion of heterotic and type I string phenomenology. The heterotic string model is based on the free--fermionic formalism. This is the first case where non--Abelian VEV's, as opposed to singlet VEV's are required for the cancellation of the Fayet--Iliopoulos term. It is noted that non--Abelian fields are the only fields that can give rise to the satisfaction of the D--flat constraints in this model. The type I models are based on T^6/Z_2x(Z_2)^s and T^6/Z_2xZ_2x(Z_2)^s compactifications. The first example has N=2 supersymmetry and includes a rank reduction of the D5 gaug…
We propose a new formulation of the heterotic $D=10$ Green-Schwarz superstring whose worldsheet is a superspace with two even and eight odd coordinates. The action is manifestly invariant under both target-space supersymmetry and a worldsheet reparametrisation supergroup. It contains only a finite set of auxiliary fields. The key ingredient are the commuting spinor (twistor) variables, which naturally arise as worldsheet superpartners of the target space Grassmann coordinates. These spinors parametrise the sphere $S^8$ regarded as a coset space of the $D=10$ Lorentz group. The sphere is associ…
In $D=3,4,6$ and 10 space--time dimensions considered is a string model invariant under transformations of $N=1$ space--time supersymmetry and $n=D-2$ local worldsheet supersymmetry with the both Virasoro constraints solved in the twistor form. The twistor solution survives in a modified form even in the presence of the heterotic fermions.
We analyse the vector bundle moduli arising from generic heterotic compactifications from the point of view of quiver representations. Phenomena such as stability walls, crossing between chambers of supersymmetry, splitting of non-Abelian bundles and dynamic generation of D-terms are succinctly encoded into finite quivers. By studying the Poincaré polynomial of the quiver moduli space using the Reineke formula, we can learn about such useful concepts as Donaldson-Thomas invariants, instanton transitions and supersymmetry breaking.
The most promising MSSM candidates of the heterotic string reveal some distinctive properties. These include gauge-top unification, a specific solution to the mu-problem and mirage pattern for the gaugino masses. The location of the top- and the Higgs-multiplets in extra dimensions differs significantly from that of the other quarks and leptons leading to a characteristic signature of suppressed soft breaking terms, reminiscent of a scheme known as natural supersymmetry.
The moduli space of toroidal type I vacua, which are consistent at the non-perturbative level, consists of independent branches characterized by the number (0, 16 or 32) of rigid branes sitting on top of orientifold planes. This structure persists also when supersymmetry is spontaneously broken a la Scherk-Schwarz. We show that all the components of the moduli space in dimension $D\ge 5$ indeed admit heterotic dual components, by explicitly constructing heterotic-type I dual pairs with the rank of the gauge group reduced by 0, 8 or 16 units. In the presence of spontaneous breaking of supersymm…
We analyze the possible dynamical emergence of IR conformal field theory describing the low- energy excitations of near-extremal black holes in five-dimensional compactification of heterotic strings. We find that, by tuning the mass and charges in such a way that the extremal black holes have a classically vanishing horizon area, the near-horizon develops an AdS3 throat and when we combine the low-energy limit with vanishing Newton coupling constant, the system has a dual conformal field theory description. We compare our results with c-extremization and the Kerr/CFT predictions.
It is argued that recent developments point to the existence of an AdS_3 x S^2 x T^5 holographic dual for the 2D CFT living on the worldsheet of N coincident heterotic strings in a T^5 compactification, which can in turn be described by an exact worldsheet CFT. A supergravity analysis is shown to imply that the global supergroup is Osp(4^*|4), with 16 supercharges and an affine extension given, surprisingly, by a nonlinear N=8 2D superconformal algebra. Possible supergroups with 16 supercharges are also found to match the expected symmetries for T^n compactification with 0<=n<=7.
In this article we review four-dimensional string vacua with N=2 space-time supersymmetry. In particular, we will discuss several aspects of the string-string duality between the heterotic string, compactified on $K3\times T^2$, and the type II superstring compactified on a Calabi-Yau three-fold. We investigate the massless supersymmetric spectra, showing agreement for a large class of dual heterotic/type II string pairs. Some emphasis is given to non-perturbative heterotic phenomena, such as non-perturbative transitions among different vacua and strong coupling singularities, and to their geo…
We study the quantum dynamics of vortex strings in N=1 SQCD with U(N_c) gauge group and N_f=N_c quarks. The classical worldsheet of the string has N=(0,2) supersymmetry, but this is broken by quantum effects. We show how the pattern of supersymmetry breaking and restoration on the worldsheet captures the quantum dynamics of the underlying 4d theory. We also find qualitative matching of the meson spectrum in 4d and the spectrum on the worldsheet.
Based on a simple adiabatic argument and by considering the heterotic string counterpart of certain symmetries of Type II superstrings such as $(-1)^{F_L}$ and orientation reversal, we construct orbifold candidates for dual pairs of heterotic and Type II string theories with $N=2$ and $N=1$ supersymmetry. We also analyze from a similar point of view the ${\rm K3}$ fibrations that enter in recently proposed $N=2$ candidates and use this structure together with certain orientation-reversing symmetries to construct $N=1$ dual pairs. These pairs involve generalizations of Type I vacua which can be…
We study possible correlations between properties of the observable and hidden sectors in heterotic string theory. Specifically, we analyze the case of the Z6-II orbifold compactification which produces a significant number of models with the spectrum of the supersymmetric standard model. We find that requiring realistic features does affect the hidden sector such that hidden sector gauge group factors SU(4) and SO(8) are favoured. In the context of gaugino condensation, this implies low energy supersymmetry breaking.
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 Gold…
We explicitly compute the entropy of an extremal dyonic black hole in heterotic string theory compactified on T^6 or K3\times T^2 by taking into account all the tree level four derivative corrections to the low energy effective action. For supersymmetric black holes the result agrees with the answer obtained earlier 1) by including only the Gauss-Bonnet corrections to the effective action 2) by including all terms related to the curvature squared terms via space-time supersymmetry transformation, and 3) by using general arguments based on the assumption of AdS_3 near horizon geometry and space…
We construct a (1,2) heterotic string with gauge symmetry and determine its particle spectrum. This theory has a local N=1 worldsheet supersymmetry for left movers and a local N=2 worldsheet supersymmetry for right movers and describes particles in either two or three space-time dimensions. We show that fermionizing the bosons of the compactified N=1 space leads to a particle spectrum which has nonabelian gauge symmetry. The fermionic formulation of the theory corresponds to a dimensional reduction of self dual Yang Mills. We also give a worldsheet action for the theory and calculate the one-l…
We compute one-loop quantum corrections to gravitational couplings in the effective action of four-dimensional heterotic strings where supersymmetry is spontaneously broken by Scherk-Schwarz fluxes. We show that in both heterotic and type II theories of this class, no moduli dependent corrections to the Planck mass are generated. We explicitly compute the one-loop corrections to the $\mathcal R^2$ coupling and find that, despite the absence of supersymmetry, its contributions may still be organised into representations of subgroups of the modular group, and admit a universal form, determined u…
It was recently shown that string theory on $\mathrm{AdS}_3 \times \mathrm{S}^3 \times \mathbb{T}^4$ with minimal NS-NS flux ($k = 1$) is exactly dual to the symmetric orbifold of T4. Here we show that a similar statement also holds for the $D_n$ orbifolds of these backgrounds that have $\mathcal{N} = (2, 2)$ supersymmetry. In this case the CFT dual is the symmetric orbifold of $\mathbb{T}^4/D_n$.
The $\mathbb{Z}_2\times \mathbb{Z}_2$ heterotic string orbifold yielded a large space of phenomenological three generation models and serves as a testing ground to explore how the Standard Model of particle physics may be incorporated in a theory of quantum gravity. In this paper we explore the existence of type 0 models in this class of string compactifications. We demonstrate the existence of type 0 $\mathbb{Z}_2\times \mathbb{Z}_2$ heterotic string orbifolds, and show that there exist a large degree of redundancy in the space of GGSO projection coefficients when the type 0 restrictions are …
Within a four-dimensional, toroidally compactified heterotic string, we identify (quantized) charge vectors of electrically charged BPS-saturated states (along with the tower of SL(2,Z) related dyonic states), which preserve 1/2 of N=4 supersymmetry and become massless along the hyper-surfaces of enhanced gauge symmetry of the two-torus moduli sub-space. In addition, we identify charge vectors of the dyonic BPS-saturated states (along with the tower of SL(2,Z) related states), which preserve 1/4 of N=4 supersymmetry, and become massless at two points with the maximal gauge symmetry enhancement…
In this paper, we study a class of heterotic Landau-Ginzburg models. We show that the action can be written as a sum of BRST-exact and non-exact terms. The non-exact terms involve the pullback of the complexified Kahler form to the worldsheet and terms arising from the superpotential, which is a Grassmann-odd holomorphic function of the superfields. We then demonstrate that the action is invariant on-shell under supersymmetry transformations up to a total derivative. Finally, we extend the analysis to the case in which the superpotential is not holomorphic. In this case, we find that supersymm…
We compute the corrections to heterotic-string backgrounds with (2,0) world-sheet supersymmetry, up to two loops in sigma-model perturbation theory. We investigate the conditions for these backgrounds to preserve spacetime supersymmetry and we find that a sufficient requirement for consistency is the applicability of the $\partial\bar\partial$-lemma. In particular, we investigate the $α'$ corrections to (2,0) heterotic-string compactifications and we find that the Calabi-Yau geometry of the internal space is deformed to a Hermitian one. We show that at first order in $α'$, the heterotic anomal…
We present a number of D=4 bosonic and heterotic string solutions with a covariantly constant null Killing vector which, like the solution of Nappi and Witten (NW), correspond to (gauged) WZW models and thus have a direct conformal field theory interpretation. A class of exact plane wave solutions (which includes the NW solution) is constructed by `boosting' the twisted products of two D=2 `cosmological' or `black-hole' cosets of SL(2,R) and SU(2). We describe a general limiting procedure by which one can construct new solutions with a covariantly constant null Killing vector starting with kno…
We use the group-theoretic interpretation of the AdS/CFT correspondence which we proposed earlier in order to lift intertwining operators acting between boundary conformal representations to intertwining operators acting between bulk conformal representations. Further, we present the classification of the positive energy (lowest weight) unitary irreducible representations of the D=6 superconformal algebras $osp(8^*/2N)$.
It is well-known that the beta functions on a string worldsheet correspond to the target space equations of motion, e.g. the Einstein equations. We show that the BPS equations, i.e. the conditions of vanishing supersymmetry variations of the space-time fermions, can be directly derived from the worldsheet. To this end we consider the RNS-formulation of the heterotic string with (2,0) supersymmetry, which describes a complex torsion target space that supports a holomorphic vector bundle. After a detailed account of its quantization and renormalization, we establish that the cancellation of the …
We study how local symmetry transformations of (p, q) anti de Sitter supergravities in three dimensions act on fields on the two-dimensional boundary. The boundary transformation laws are shown to be the same as those of two-dimensional (p, q) conformal supergravities for p, q \leq 2. Weyl and super Weyl transformations are generated from three-dimensional general coordinate and super transformations.
We calculate near-horizon solutions for four-dimensional 4-charge and five-dimensional 3-charge black holes in heterotic string theory from the part of the ten-dimensional tree-level effective action which is connected to gravitational Chern-Simons term by supersymmetry. We obtain that the entropies of large black holes exactly match the alpha'-exact statistical entropies obtained from microstate counting (D=4) and AdS/CFT correspondence (D=5). Especially interesting is that we obtain agreement for both BPS and non-BPS black holes, contrary to the case of R^2-truncated (four-derivative) action…
The computation of $κ$-anomalies in the Green-Schwarz heterotic superstring sigma-model and the corresponding Wess-Zumino consistency condition constitute a powerful alternative approach for the derivation of manifestly supersymmetric string effective actions. With respect to the beta-function approach this technique presents the advantage that a result which is obtained with the computation of beta-functions at $n$ loops can be obtained through the calculation of $κ$-anomalies at \hbox{$n-1$} loops. In this paper we derive by a direct one-loop perturbative computation the $κ$-anomaly associat…
We propose an action describing chiral fermions with an arbitrary gauge group and with manifest $(8,0)$ worldsheet supersymmetry. The form of the action is inspired by and adapted for completing the twistor-like formulation of the $D=10$ heterotic superstring.
