Space-time Supersymmetry Research Articles

Massless particles on supergroups and AdS 3 × S 3 supergravity

Firstly, we study the state space of a massless particle on a supergroup with a reparameterization invariant action. After gauge fixing the reparameterization invariance, we compute the physical state space through the BRST cohomology and show that the quadratic Casimir Hamiltonian becomes diagonalizable in cohomology. We illustrate the general mechanism in detail in the example of a supergroup target GL(1|1). The space of physical states remains an indecomposable infinite dimensional representation of the space-time supersymmetry algebra. Secondly, we show how the full string BRST cohomology in the particle limit of string theory on AdS3 x S3 renders the quadratic Casimir diagonalizable, and reduces the Hilbert space to finite dimensional representations of the space-time supersymmetry algebra (after analytic continuation). Our analysis provides an efficient way to calculate the Kaluza-Klein spectrum for supergravity on AdS3 x S3. It may also be a step towards the identification of an interesting and simpler subsector of logarithmic supergroup conformal field theories, relevant to string theory.

Conformal aspects of Spinor–Vector duality

We present a detailed study of various aspects of Spinor–Vector duality in Heterotic string compactifications and expose its origin in terms of the internal conformal field theory. In particular, we illustrate the main features of the duality map by using simple toroidal orbifolds preserving N 4 = 1 and N 4 = 2 spacetime supersymmetries in four dimensions. We explain how the duality map arises in this context by turning on special values of the Wilson lines around the compact cycles of the manifold. We argue that in models with N 4 = 2 spacetime supersymmetry, the interpolation between the Spinor–Vector dual vacua can be continuously realized. We trace the origin of the Spinor–Vector duality map to the presence of underlying N = ( 2 , 2 ) and N = ( 4 , 4 ) SCFTs, and explicitly show that the induced spectral flow in the twisted sectors is responsible for the observed duality. The isomorphism between current algebra representations gives rise to a number of chiral character identities, reminiscent of the recently-discovered MSDS symmetry.

Computing the spectrum of a heterotic flux vacuum

We compute the massless spectra of a set of flux vacua of the heterotic string. The vacua we study include well-known non-Kahler T^2-fibrations over K3 with SU(3) structure and intrinsic torsion. Following gauged linear sigma models of these vacua into phases governed by asymmetric Landau-Ginzburg orbifolds allows us to compute the spectrum using generalizations of familiar LG-orbifold techniques. We study several four- and six-dimensional examples with N=2 spacetime supersymmetry in detail.

An algebraic model for the $ \mathfrak{s}\mathfrak{u}\left( {\left. 2 \right|2} \right) $ Light-Cone string field theory

We investigate algebraic structure of light-cone string field theory which respects the spacetime supersymmetry \( \mathfrak{s}\mathfrak{u}\left( {\left. 2 \right|2} \right) \). Extracting building blocks from the explicit oscillator expressions of light-cone superstring field theory on the pp-wave and the flat background, we propose a model for more generic backgrounds by giving an algebraic procedure to construct supercharges and Hamiltonian without referring to explicit oscillator expressions. Based on this strategy, we systematically construct interaction terms of light-cone string field theory on the pp-wave background and some examples of its generalization. We also study the supergravity limit of the interaction terms on the pp-wave background.

Model of M-theory with eleven matrices

We show that an action of a supermembrane in an eleven-dimensional spacetime with a semi-light-cone gauge can be written only with Nambu-Poisson bracket and an invariant symmetric bilinear form under an approximation. Thus, the action under the conditions is manifestly covariant under volume preserving diffeomorphism even when the world-volume metric is flat. Next, we propose two 3-algebraic models of M-theory which are obtained as a second quantization of an action that is equivalent to the supermembrane action under the approximation. The second quantization is defined by replacing Nambu-Poisson bracket with finite-dimensional 3-algebras' brackets. Our models include eleven matrices corresponding to all the eleven space-time coordinates in M-theory although they possess not SO(1,10) but SO(1,2) x SO(8) or SO(1,2) x SU(4) x U(1) covariance. They possess N=1 space-time supersymmetry in eleven dimensions that consists of 16 kinematical and 16 dynamical ones. We also show that the SU(4) model with a certain algebra reduces to BFSS matrix theory if DLCQ limit is taken.

Non-Abelian Gauge Field Localized on Walls with Four-Dimensional World Volume

A mechanism using the position-dependent gauge coupling is proposed to localize non-Abelian gauge fields on domain walls in five-dimensional space-time. Low-energy effective theory posseses a massless vector field, and a mass gap. The four-dimensional gauge invariance is maintained intact. We obtain perturbatively the four-dimensional Coulomb law for static sources on the domain wall. BPS domain wall solutions with the localization mechanism are explicitly constructed in the U(1)xU(1) supersymmetric gauge theory coupling to the non-Abelian gauge fields only through the cubic prepotential, which is consistent with the general principle of supersymmetry in five-dimensional space-time.

Getting superstring amplitudes by degenerating Riemann surfaces

We explicitly show how the chiral superstring amplitudes can be obtained through factorisation of the higher genus chiral measure induced by suitable degenerations of Riemann surfaces. This powerful tool also allows to derive, at any genera, consistency relations involving the amplitudes and the measure. A key point concerns the choice of the local coordinate at the node on degenerate Riemann surfaces that greatly simplifies the computations. As a first application, starting from recent ansätze for the chiral measure up to genus five, we compute the chiral two-point function for massless Neveu–Schwarz states at genus two, three and four. For genus higher than three, these computations include some new corrections to the conjectural formulae appeared so far in the literature. After GSO projection, the two-point function vanishes at genus two and three, as expected from space–time supersymmetry arguments, but not at genus four. This suggests that the ansatz for the superstring measure should be corrected for genus higher than four.

Marginal deformations of vacua with massive boson–fermion degeneracy symmetry

Two-dimensional string vacua with Massive Spectrum boson–fermion Degeneracy Symmetry, [ MSDS ] d = 2 , are explicitly constructed in Type II and Heterotic superstring theories. The study of their moduli space indicates the existence of large marginal deformations that connect continuously the initial [ MSDS ] d = 2 vacua to higher-dimensional conventional superstring vacua, where spacetime supersymmetry is spontaneously broken by geometrical fluxes. We find that the maximally symmetric, [ Max : MSDS ] d = 2 , Type II vacuum, is in correspondence with the maximal, N = 8 , d = 4 “gauged supergravity”, where the supergravity gauging is induced by the fluxes. This correspondence is extended to less symmetric cases where the initial MSDS symmetry is reduced by orbifolds: [ Z orb : MSDS ] d = 2 ↔ [ N ⩽ 8 : SUGRA ] d = 4 , fluxes . We also exhibit and analyse thermal interpretations of some Euclidean versions of the models and identify classes of MSDS vacua that remain tachyon-free under arbitrary marginal deformations about the extended symmetry point. The connection between the two-dimensional MSDS vacua and the resulting four-dimensional effective supergravities arises naturally within the context of an adiabatic cosmological evolution, where the very early Universe is conjectured to be described by an MSDS vacuum, while at late cosmological times it is described by an effective N = 1 supergravity theory with spontaneously broken supersymmetry.

Supersymmetry breaking, heterotic strings and fluxes

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 supersymmetry. In this case the differential equation is of Laplace type and as a result the solvability is guaranteed.

Induced superstring cosmologies and moduli stabilization

We extend the analysis of the recently obtained stringy cosmological solutions induced by thermal and quantum effects, once space–time supersymmetry is spontaneously broken by geometrical fluxes. Cases in which more than one modulus participating in the supersymmetry breaking mechanism are investigated. The free energy is obtained at the full string level. In the intermediate cosmological region where the temperature and the supersymmetry breaking scale are sufficiently smaller than the Hagedorn temperature, the quantum and thermal corrections are under control and calculable. The reason is that the contributions to the effective potential of the moduli that are not participating in the supersymmetry breaking are exponentially suppressed. The backreaction on the initially flat background results in many cases into cosmological evolutions, where the dynamics of all complex structure moduli is frozen. The solutions describe effectively a radiation dominated era, where thermal effects are never negligible, even if the temperature tends to zero at late times. We analyze several types of supersymmetry breaking patterns and examine the stability of the corresponding radiation era.

Non-supersymmetric orientifolds of Gepner models

Starting from a previously collected set of tachyon-free closed strings, we search for N=2 minimal model orientifold spectra which contain the standard model and are free of tachyons and tadpoles at lowest order. For each class of tachyon-free closed strings – bulk supersymmetry, automorphism invariants or Klein bottle projection – we do indeed find non-supersymmetric and tachyon free chiral brane configurations that contain the standard model. However, a tadpole-cancelling hidden sector could only be found in the case of bulk supersymmetry. Although about half of the examples we have found make use of branes that break the bulk space–time supersymmetry, the resulting massless open string spectra are nevertheless supersymmetric in all cases. Dropping the requirement that the standard model be contained in the spectrum, we find chiral tachyon and tadpole-free solutions in all three cases, although in the case of bulk supersymmetry all massless spectra are supersymmetric. In the other two cases we find truly non-supersymmetric spectra, but a large fraction of them are nevertheless partly or fully supersymmetric at the massless level.

Recursion relations from space-time supersymmetry

We describe a method for obtaining relations between higher derivative interactions in supersymmetric effective actions. The method extends to all orders in the momentum expansion. As an application, we consider the string coupling dependence of the \hat{G}^{2k} \lambda^{16} interaction in type IIB string theory. Using supersymmetry, we show that each of these interactions satisfies a Poisson equation on the moduli space with sources determined by lower momentum interactions. We argue that these protected couplings are only renormalized by a finite number of string loops together with non-perturbative terms. Finally, we explore some consequences of the Poisson equation for low values of k.

M-theory superalgebra from multiple membranes

We investigate space-time supersymmetry of the model of multiple M2-branes proposed by Bagger-Lambert and Gustavsson. When there is a central element in Lie 3-algebra, the model possesses an extra symmetry shifting the fermions in the central element. Together with the original worldvolume supersymmetry transformation, we construct major part of the eleven dimensional space-time super-Poincare algebra with central extensions. Implications to transverse five-branes in the matrix model for M-theory are also discussed.

Is SUSY natural?

Space-time supersymmetry (SUSY) is widely believed to play an important role in most fundamental theories of physics, and is usually invoked in order to address problems of naturalness. In this paper, we examine the question of whether SUSY itself is ‘natural’ (i.e. likely to exist as a fundamental component of nature at high-energy scales). Our approach to answering this question is based on a statistical examination of the heterotic string landscape, and our conclusion is that SUSY is an exceedingly rare phenomenon. We also find that the likelihood of SUSY appearing at the string scale is dependent on the gauge symmetries present at the string scale, with certain gauge groups strongly favoring the appearance of SUSY and others not. This paper summarizes several recent papers, yet also contains some new results. In particular, one new result is that the heterotic landscape appears to favor either the non-supersymmetric Standard Model or an SUSY GUT gauge group at the string scale; by contrast, the opposite outcomes (namely the minimal supersymmetric Standard Model (MSSM) or a non-supersymmetric GUT) are significantly disfavored.

Non-standard supersymmetries on spaces admitting Killing–Yano tensors

We attempt to point out the intimate relation between Killing–Yano tensors and non-standard supersymmetries, along the way reviewing some recent results. The Euclidean Taub–NUT space is taken to illustrate some of the aspects of the general discussion about the connection between spacetime higher order geometrical symmetries and supersymmetries. The dynamical symmetry of this space leads in a natural way to an infinite dimensional twisted loop superalgebra of the conserved operators.

Spinor-vector duality in [formula omitted] heterotic string vacua

Classification of the N = 1 space–time supersymmetric fermionic Z 2 × Z 2 heterotic-string vacua with symmetric internal shifts, revealed a novel spinor-vector duality symmetry over the entire space of vacua, where the S t ↔ V duality interchanges the spinor plus anti-spinor representations with vector representations. In this paper we demonstrate that the spinor-vector duality exists also in fermionic Z 2 heterotic string models, which preserve N = 2 space–time supersymmetry. In this case the interchange is between spinorial and vectorial representations of the unbroken SO ( 12 ) GUT symmetry. We provide a general algebraic proof for the existence of the S t ↔ V duality map. We present a novel basis to generate the free fermionic models in which the ten-dimensional gauge degrees of freedom are grouped into four groups of four, each generating an SO ( 8 ) modular block. In the new basis the GUT symmetries are produced by generators arising from the trivial and non-trivial sectors, and due to the triality property of the SO ( 8 ) representations. Thus, while in the new basis the appearance of GUT symmetries is more cumbersome, it may be more instrumental in revealing the duality symmetries that underly the string vacua.

Bosonized supersymmetry from the Majorana-Dirac-Staunton theory and massive higher-spin fields

We propose a (3+1)D linear set of covariant vector equations, which unify the spin-0 'new Dirac equation' with its spin-1/2 counterpart, proposed by Staunton. Our equations describe a spin-(0,1/2) supermultiplet with different numbers of degrees of freedom in the bosonic and fermionic sectors. The translation-invariant spin degrees of freedom are carried by two copies of the Heisenberg algebra. This allows us to realize space-time supersymmetry in a bosonized form. The grading structure is provided by an internal reflection operator. Then the construction is generalized by means of the Majorana equation to a supersymmetric theory of massive higher-spin particles. The resulting theory is characterized by a nonlinear symmetry superalgebra, that, in the large-spin limit, reduces to the super-Poincare algebra with or without tensorial central charge.

Dirac-type operators on curved spaces admitting Killing-Yano tensors

We attempt to point out the relation between Killing-Yano tensors and non-standard supersymmetries. The Killing-Yano tensors play an important role in the Dirac theory on curved spaces where they produce Dirac-type operators. The Euclidean Taub-NUT space is taken to illustrate some of the aspects of the general discussion about the connection between spacetime higher order geometrical symmetries and supersymmetries. The dynamical symmetry of this space leads in a natural way to an infinite dimensional twisted loop superalgebra of the conserved operators.

Dimension-changing exact solutions of string theory

Superstring theories in the critical dimension D=10 are connected to one another by a well-explored web of dualities. In this paper we use closed-string tachyon condensation to connect the supersymmetric moduli space of the critical superstring to non-supersymmetric string theories in more than ten dimensions. We present a new set of classical solutions that exhibit dynamical transitions between string theories in different dimensions, with different degrees of stability and different amounts of spacetime supersymmetry. In all examples, the string-frame metric and dilaton gradient readjust themselves during the transition. The central charge of the worldsheet theory remains equal to 15, even as the total number of dimensions changes. This phenomenon arises entirely from a one-loop diagram on the string worldsheet. Allowed supersymmetric final states include half-BPS vacua of type II and SO(32) heterotic string theory. We also find solutions that bypass the critical dimension altogether and proceed directly to spacelike linear dilaton theories in dimensions greater than or equal to two.

Dying dyons don't count

The dyonic 1/4-BPS states in 4D string theory with = 4 spacetime supersymmetry are counted by a Siegel modular form. The pole structure of the modular form leads to a contour dependence in the counting formula obscuring its duality invariance. We exhibit the relation between this ambiguity and the (dis-)appearance of bound states of 1/2-BPS configurations. Using this insight we propose a precise moduli-dependent contour prescription for the counting formula. We then show that the degeneracies are duality-invariant and are correctly adjusted at the walls of marginal stability to account for the (dis-)appearance of the two-centered bound states. Especially, for large black holes none of these bound states exists at the attractor point and none of these ambiguous poles contributes to the counting formula. Using this fact we also propose a second, moduli-independent contour which counts the ``immortal dyons that are stable everywhere.