Space-time Supersymmetry Research Articles

Anomaly constraints for heterotic strings and supergravity in six dimensions

The landscape of six-dimensional supergravities is dramatically constrained by the cancellation of gauge and gravitational anomalies, but the full extent of its implications has not been uncovered. We explore the cancellation of global anomalies of the Dai-Freed type in this setting with abelian and simply laced gauge groups, finding novel constraints. In particular, we exclude arbitrarily large abelian charges in an infinite family of theories for certain types of quadratic refinements, including a specific one defined in the literature. We also show that the Gepner orientifold with no tensor multiplets is anomaly-free for a different choice, as well as a number of heterotic models with and without spacetime supersymmetry in six dimensions. The latter analysis extends previous results in ten dimensions to some lower-dimensional settings in the heterotic landscape.

From free-fermionic constructions to orbifolds and back

We systematically develop the explicit map between string vacua constructed in the Free Fermionic Formulation and their ℤ2N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\mathbb{Z}}_2^N $$\\end{document} toroidal orbifold counterparts. We illustrate the map in various example classes of models, including cases relevant for string phenomenology, as well as in theories where space-time supersymmetry is broken by the stringy Scherk-Schwarz mechanism.

Mirror symmetry and new approach to constructing orbifolds of Gepner models

Motivated by the principles of the conformal bootstrap, primarily the principle of Locality, simultaneously with the requirement of space-time supersymmetry, we reconsider constructions of compactified superstring models. Starting from requirements of space-time supersymmetry and mutual locality, we construct a complete set of physical fields of orbifolds of Gepner models. To technically implement this, we use spectral flow generators to construct all physical fields from the chiral primary fields. The set of these spectral flow operators forms a so-called admissible group Gadm, which defines a given orbifold. The action of these operators produces a collection of physical fields consistent with the action of supersymmetry generators. The selection of mutually local fields from this collection is carried out using the mirror group Gadm⁎. The permutation of Gadm and Gadm⁎ replaces the original orbifold with a mirror one that satisfies the same conditions as the original one. This also implies that the resulting model is modular invariant.

Celestial Supersymmetry

We discuss supersymmetric Yang-Mills theory coupled to dilatons in the framework of celestial holography. We show that in the presence of point-like dilaton sources, the CCFT operators associated with the gauge supermultiplet acquire a simple, factorized form. They factorize into the holomorphic (super)current part and the exponential “light” operators of Liouville theory, in the infinite central charge limit. The current sector exhibits (1,0) supersymmetry, thus implementing spacetime supersymmetry in CCFT.

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.

Revisiting Dudas-Mourad Compactifications

Superstring theories in ten dimensions allow spacetime supersymmetry breaking at the string scale at the expense of controlled Minkowski backgrounds. The next-to-maximally symmetric backgrounds, found by Dudas and Mourad, involve a warped compactification on an interval associated with codimension-one defects. We generalize these solutions by varying the effective field theory parameters, and we discuss the dimensional reduction on the interval. In particular, we show that scalars and form fields decouple in a certain range of dimensions, yielding Einstein-Yang-Mills theory. Moreover, we find that the breakdown of this effective description due to light Kaluza-Klein modes reflects the swampland distance conjecture, supporting the consistency of the picture at least qualitatively.

4D supersymmetric gauge theories of spacetime translations

The paper addresses the question whether in four spacetime dimensions, besides standard supergravity theories, field theories exist whose symmetries include local spacetime translations and supersymmetries generated by transformations whose commutators contain infinitesimal local spacetime translations. Several new supersymmetric free field theories are found which may provide theories of that type. It is outlined how these free field theories may be extended to globally supersymmetric theories with the desired properties. One class of such theories is constructed explicitly. These theories are similar to globally supersymmetric Yang-Mills theories in flat spacetime but have supersymmetries generated by transformations whose commutators generate infinitesimal general coordinate transformations with field dependent gauge parameters.

Complete nonlinear action for a supersymmetric multiple D0-brane system

We present a complete nonlinear action for the dynamical system of nearly coincident multiple D$0$-branes (mD$0$) which possesses, besides manifest spacetime (target superspace) supersymmetry, also the worldline supersymmetry, a counterpart of the local fermionic $\kappa$-symmetry of single D$0$-brane (Dirichlet superparticle). The action contains an arbitrary non-vanishing function ${\cal M}({\cal H})$ of the relative motion Hamiltonian ${\cal H}$. The $D=10$ mD$0$ model with particular form of ${\cal M}({\cal H})$ can be obtained by dimensional reduction from the action of eleven-dimensional ($D=11$) multiple M-wave (mM$0$) system.

Emergent space-time supersymmetry at disordered quantum critical points

We study the effect of disorder on the space-time supersymmetry that is proposed to emerge at the quantum critical point of pair density wave transition in $(2+1)$-dimensional (D) Dirac semimetals and $(3+1)$D Weyl semimetals. In the $(2+1)$D Dirac semimetal, we consider three types of disorder, including random scalar potential, random vector potential and random mass potential, whereas the random mass disorder is absent in the $(3+1)$D Weyl semimetal. Via a systematic renormalization-group analysis, we find that any type of weak random disorder is irrelevant due to the couplings between the disorder potential and the Yukawa vertex. The emergent supersymmetry is, thus, stable against weak random potentials. Our paper will pave the way for exploration supersymmetry in realistic condensed-matter systems.

BPS Algebras in 2D String Theory

We discuss a set of heterotic and type II string theory compactifications to 1+1 dimensions that are characterized by factorized internal worldsheet CFTs of the form V_1otimes bar{V}_2, where V_1, V_2 are self-dual (super) vertex operator algebras. In the cases with spacetime supersymmetry, we show that the BPS states form a module for a Borcherds–Kac–Moody (BKM) (super)algebra, and we prove that for each model the BKM (super)algebra is a symmetry of genus zero BPS string amplitudes. We compute the supersymmetric indices of these models using both Hamiltonian and path integral formalisms. The path integrals are manifestly automorphic forms closely related to the Borcherds–Weyl–Kac denominator. Along the way, we comment on various subtleties inherent to these low-dimensional string compactifications.

3D supersymmetric nonlinear multiple D0-brane action and 4D counterpart of multiple M-wave system

Found is the complete nonlinear action of multiple D0-brane system (mD0) in three dimensional type II superspace which is invariant under rigid D = 3 mathcal{N} = 2 spacetime supersymmetry and under local worldline supersymmetry generalizing the κ-symmetry of single D0-brane action. We show that a particular representative of this family of actions can be obtained by dimensional reduction of the action of D = 4 non-Abelian multiwaves (nAmW), the D = 4 counterpart of 11D multiple M-wave (mM0) action, that we have also constructed in this paper. This reduction results in an action with is nonlinear due to the presence of a certain function ℳ(ℋ) of the relative motion Hamiltonian ℋ, the counterpart of which enters the 4D nAmW action linearly. Curiously, the action possesses double supersymmetry also for an arbitrary function ℳ(ℋ). In particular for ℳ = const we find a dynamical system describing the sum of single D0 action and the action of 1d dimensional reduction of the D = 3 mathcal{N} = 2 SYM coupled to the worldline supergravity induced by the embedding of the center of energy motion into the D = 3 mathcal{N} = 2 superspace.

Calculating the Higgs mass in string theory

In this paper, we establish a fully string-theoretic framework for calculating one-loop Higgs masses directly from first principles in perturbative closed string theories. Our framework makes no assumptions other than worldsheet modular invariance and is therefore applicable to all closed strings, regardless of the specific string construction utilized. This framework can also be employed even when spacetime supersymmetry is broken (and even when this breaking occurs at the Planck scale), and can be utilized for all scalar Higgs fields, regardless of the particular gauge symmetries they break. This therefore includes the Higgs field responsible for electroweak symmetry breaking in the Standard Model. Notably, using our framework, we demonstrate that a gravitational modular anomaly generically relates the Higgs mass to the one-loop cosmological constant, thereby yielding a string-theoretic connection between the two fundamental quantities which are known to suffer from hierarchy problems in the absence of spacetime supersymmetry. We also discuss a number of crucial issues involving the use and interpretation of regulators in UV/IR-mixed theories such as string theory, and the manner in which one can extract an EFT description from such theories. Finally, we analyze the running of the Higgs mass within such an EFT description, and uncover the existence of a "dual IR" region which emerges at high energies as the consequence of an intriguing scale-inversion duality symmetry. We also identify a generic stringy effective potential for the Higgs fields in such theories. Our results can therefore serve as the launching point for a rigorous investigation of gauge hierarchy problems in string theory.

Higher-spin states of the superstring in an electromagnetic background

Constructing a consistent four-dimensional Lagrangian for charged massive higher-spin fields propagating in an electromagnetic background is an open problem. In 1989, Argyres and Nappi used bosonic open string field theory to construct a Lagrangian for charged massive spin-2 fields in a constant electromagnetic background. In this paper, we use the four-dimensional hybrid formalism for open superstring field theory to construct a supersymmetric Lagrangian for charged massive spin-2 and spin-3/2 fields in a constant electromagnetic background. The hybrid formalism has the advantage over the RNS formalism of manifest mathcal{N} = 1 d=4 spacetime supersymmetry so that the spin-2 and spin-3/2 fields are combined into a single superfield and there is no need for picture-changing or spin fields.

Manifest spacetime supersymmetry and the superstring

The algebra of spacetime supersymmetry generators in the RNS formalism for the superstring closes only up to a picture-changing operation. After adding non-minimal variables and working in the “large” Hilbert space, the algebra closes without picture-changing and spacetime supersymmetry can be made manifest. The resulting non-minimal version of the RNS formalism is related by a field redefinition to the pure spinor formalism.

Implications of New Physics Models for the Couplings of the Higgs Boson

It has been almost a decade since the first hints of the Higgs boson discovery began to emerge from CERN, making a review of our updated expectations for the Higgs boson properties, in light of New Physics models, timely. In this review I attempt to draw connections between modified Higgs boson couplings and the big questions that broad classes of New Physics models aim to answer. Questions considered include whether the Higgs boson is composite and whether a new space-time supersymmetry exists. The goal is to present these topics, framed in reference to the Higgs boson, in a conceptually driven manner and, to make them accessible to a relatively broad audience, without a great deal of technicality.

Stable vacua for tachyonic strings

In addition to the familiar string theories with spacetime supersymmetry, there exist a number of non-supersymmetric ten-dimensional superstrings. Nearly all of these theories have closed string tachyons, indicating a misidentification of the vacuum around which they are to be quantized. In this work, we identify (meta)stable vacua for all known tachyonic superstrings. These vacua are all lower-dimensional, with most of them being familiar two-dimensional string theories. However, there are also intriguing examples of solutions in dimensions 6, 8, and 9, with respective gauge groups $E_7 \times E_7$, $SU(16)$, and $E_8$. These special vacua have positive vacuum energy and no moduli.

Boundary contributions to three loop superstring amplitudes

In type II superstring theory, the vacuum amplitude at a given loop order g can receive contributions from the boundary of the compactified, genus g supermoduli space of curves M̄g. These contributions capture the long distance or infrared behavior of the amplitude. The boundary parameterizes degenerations of genus g super Riemann surfaces. A holomorphic projection of the supermoduli space onto its reduced space would then provide a way to integrate the holomorphic, superstring measure and thereby give the superstring vacuum amplitude at g-loop order. However, such a projection does not generally exist over the bulk of the supermoduli spaces in higher genera. Nevertheless, certain boundary divisors in ∂M̄g may holomorphically map onto a bosonic space upon composition with universal morphisms, thereby enabling an integration of the holomorphic, superstring measure here. Making use of ansatz factorizations of the superstring measure near the boundary, our analysis shows that the boundary contributions to the three loop vacuum amplitude will vanish in closed oriented type II superstring theory with unbroken spacetime supersymmetry.

Towards the classification of tachyon-free models from tachyonic ten-dimensional heterotic string vacua

Recently it was proposed that ten-dimensional tachyonic string vacua may serve as starting points for the construction of viable four dimensional phenomenological string models which are tachyon–free. This is achieved by projecting out the tachyons in the four-dimensional models using projectors other than the projector which is utilised in the supersymmetric models and those of the SO(16)×SO(16) heterotic string. We continue the exploration of this class of models by developing systematic computerised tools for their classification, the analysis of their tachyonic and massless spectra, as well as analysis of their partition functions and vacuum energy. We explore a randomly generated space of 2×109 string vacua in this class and find that tachyon–free models occur with ∼5×10−3 probability, and of those, phenomenologically inclined SO(10) vacua with a00=Nb0−Nf0=0, i.e. equal number of fermionic and bosonic massless states, occur with frequency ∼2×10−6. Extracting larger numbers of phenomenological vacua therefore requires adaptation of fertility conditions that we discuss, and significantly increase the frequency of tachyon–free models. Our results suggest that spacetime supersymmetry may not be a necessary ingredient in phenomenological string models, even at the Planck scale.

Finite W-superalgebras and quadratic spacetime supersymmetries

We consider Lie superalgebras under constraints of Hamiltonian reduction, yielding finite W-superalgebras which provide candidates for quadratic spacetime superalgebras. These have an undeformed bosonic symmetry algebra (even generators) graded by a fermionic sector (supersymmetry generators) with anticommutator brackets which are quadratic in the even generators. We analyze the reduction of several Lie superalgebras of type gl(M|N) or osp(M|2N) at the classical (Poisson bracket) level, and also establish their quantum (Lie bracket) equivalents. Purely bosonic extensions are also considered. As a special case we recover a recently identified quadratic superconformal algebra, certain of whose unitary irreducible massless representations (in four dimensions) are ‘zero-step’ multiplets, with no attendant superpartners. Other cases studied include a six dimensional quadratic superconformal algebra with vectorial odd generators, and a variant quadratic superalgebra with undeformed osp(1|2N) singleton supersymmetry, and a triplet of spinorial supercharges.

Mathcal{SW}left(frac{3}{2},2right) subsymmetry in G2, Spin(7) and mathcal{N} = 2 CFTs

Spectral flow, spacetime supersymmetry, topological twists, chiral primaries related to marginal deformations, mirror symmetry: these are important consequences of the worldsheet mathcal{N} = 2 superconformal symmetry of strings on Calabi-Yau manifolds. To various degrees of certainty, these features were also established when the target is either 7d or 8d with exceptional holonomy G2 or Spin(7) respectively. We show that these are more than mere analogies. We exhibit an underlying symmetry mathcal{SW}left(frac{3}{2},2right) making a bridge between the latter cases and K3 target spaces. Reviewing unitary representations of mathcal{SW}left(frac{3}{2},2right) leads us to speculate on further roles of this algebra in string theory compactifications and on the existence of topologically twisted versions of mathcal{SW}left(frac{3}{2},2right) theories.