Spin projection operators and higher-spin Cotton tensors in three dimensions
We elaborate on the spin projection operators in three dimensions and use them to derive a new representation for the linearised higher-spin Cotton tensors.
hep-th↗
arXiv subjects
Evgeny I. Buchbinder
Publications and source records attributed to Evgeny I. Buchbinder.
Higher spin supercurrents in anti-de Sitter space
We propose higher spin supercurrent multiplets for ${\cal N}=1$ supersymmetric field theories in four-dimensional anti-de Sitter space (AdS). Their explicit realisations are derived for various supersymmetric theories, including a model of $N$ massive chiral scalar superfields with an arbitrary mass matrix. We also present new off-shell gauge formulations for the massless ${\cal N}=1$ supersymmetric multiplet of integer superspin $s$ in AdS, where $s =2,3,\dots$, as well as for the massless gravitino multiplet (superspin $s=1$) which requires special consideration.
hep-th↗
Non-vanishing Heterotic Superpotentials on Elliptic Fibrations
We present models of heterotic compactification on Calabi-Yau threefolds and compute the non-perturbative superpotential for vector bundle moduli. The key feature of these models is that the threefolds, which are elliptically fibered over del Pezzo surfaces, have homology classes with a unique holomorphic, isolated genus-zero curve. Using the spectral cover construction, we present vector bundles for which we can explicitly calculate the Pfaffians associated with string instantons on these curves. These are shown to be non-zero, thus leading to a non-vanishing superpotential in the 4D effective action. We discuss, in detail, why such compactifications avoid the Beasley-Witten residue theorem.
hep-th↗
Matter Field Kahler Metric in Heterotic String Theory from Localisation
We propose an analytic method to calculate the matter field Kähler metric in heterotic compactifications on smooth Calabi-Yau three-folds with Abelian internal gauge fields. The matter field Kähler metric determines the normalisations of the ${\cal N}=1$ chiral superfields, which enter the computation of the physical Yukawa couplings. We first derive the general formula for this Kähler metric by a dimensional reduction of the relevant supergravity theory and find that its T-moduli dependence can be determined in general. It turns out that, due to large internal gauge flux, the remaining integrals localise around certain points on the compactification manifold and can, hence, be calculated approximately without precise knowledge of the Ricci-flat Calabi-Yau metric. In a final step, we show how this local result can be expressed in terms of the global moduli of the Calabi-Yau manifold. The method is illustrated for the family of Calabi-Yau hypersurfaces embedded in $\mathbb{P}^1\times\mathbb{P}^3$ and we obtain an explicit result for the matter field Kähler metric in this case.
hep-th↗
Two-form supergravity, superstring couplings, and Goldstino superfields in three dimensions
We develop off-shell formulations for ${\cal N}=1$ and ${\cal N}=2$ anti-de Sitter supergravity theories in three spacetime dimensions that contain gauge two-forms in the auxiliary field sector. These formulations are shown to allow consistent couplings of supergravity to the Green-Schwarz superstring with ${\cal N}=1$ or ${\cal N}=2$ spacetime supersymmetry. In addition to being $κ$-symmetric, the Green-Schwarz superstring actions constructed are also invariant under super-Weyl transformations of the target space. We also present a detailed study of models for spontaneously broken local supersymmetry in three dimensions obtained by coupling the known off-shell ${\cal N}=1$ and ${\cal N}=2$ supergravity theories to nilpotent Goldstino superfields.
hep-th↗
Three-form multiplet and supersymmetry breaking
Recently, a nilpotent real scalar superfield $V$ was introduced in arXiv:1702.02423 as a model for the Goldstino. It contains only two independent component fields, the Goldstino and the auxiliary $D$-field. Here we first show that $V$ can equivalently be realised as a constrained three-form superfield. We demonstrate that every irreducible Goldstino superfield (of which the Goldstino is the only independent component field) can be realised as a descendant of $V$ which is invariant under local rescalings $V \to {\rm e}^τV$, where $τ$ is an arbitrary real scalar superfield. We next propose a new Goldstino supermultiplet which is described by a nilpotent three-form superfield $\cal Y$ that is a variant formulation for the nilpotent chiral superfield, which is often used in off-shell models for spontaneously broken supergravity. It is shown that the action describing the dynamics of $\cal Y$ may be obtained from a supersymmetric nonlinear $σ$-model in the infrared limit. Unlike $V$, the Goldstino superfield $\cal Y$ contains two independent auxiliary fields, $F= H+{\rm i} G$, of which $H$ is a scalar and $G$ is the field strength of a gauge three-form. When $\cal Y$ is coupled to supergravity, both $H$ and $G$ produce positive contributions to the cosmological constant. While the contribution from $H$ is uniquely determined by the parameter of the supersymmetry breaking in the action, the contribution from $G$ is dynamical.
hep-th↗
Holomorphic Yukawa Couplings for Complete Intersection Calabi-Yau Manifolds
We develop methods to compute holomorphic Yukawa couplings for heterotic compactifications on complete intersection Calabi-Yau manifolds, generalising results of an earlier paper for Calabi-Yau hypersurfaces. Our methods are based on constructing the required bundle-valued forms explicitly and evaluating the relevant integrals over the projective ambient space. We also show how our approach relates to an earlier, algebraic one to calculate the holomorphic Yukawa couplings. A vanishing theorem, which we prove, implies that certain Yukawa couplings allowed by low-energy symmetries are zero due to topological reasons. To illustrate our methods, we calculate Yukawa couplings for SU(5)-based standard models on a co-dimension two complete intersection manifold.
hep-th↗
Non-vanishing Superpotentials in Heterotic String Theory and Discrete Torsion
We study the non-perturbative superpotential in E_8 x E_8 heterotic string theory on a non-simply connected Calabi-Yau manifold X, as well as on its simply connected covering space \tilde{X}. The superpotential is induced by the string wrapping holomorphic, isolated, genus 0 curves. According to the residue theorem of Beasley and Witten, the non-perturbative superpotential must vanish in a large class of heterotic vacua because the contributions from curves in the same homology class cancel each other. We point out, however, that in certain cases the curves treated in the residue theorem as lying in the same homology class, can actually have different area with respect to the physical Kahler form and can be in different homology classes. In these cases, the residue theorem is not directly applicable and the structure of the superpotential is more subtle. We show, in a specific example, that the superpotential is non-zero both on \tilde{X} and on X. On the non-simply connected manifold X, we explicitly compute the leading contribution to the superpotential from all holomorphic, isolated, genus 0 curves with minimal area. The reason for the non-vanishing of the superpotental on X is that the second homology class contains a finite part called discrete torsion. As a result, the curves with the same area are distributed among different torsion classes and, hence, do not cancel each other.
hep-th↗
Holomorphic Yukawa Couplings in Heterotic String Theory
We develop techniques, based on differential geometry, to compute holomorphic Yukawa couplings for heterotic line bundle models on Calabi-Yau manifolds defined as complete intersections in projective spaces. It is shown explicitly how these techniques relate to algebraic methods for computing holomorphic Yukawa couplings. We apply our methods to various examples and evaluate the holomorphic Yukawa couplings explicitly as functions of the complex structure moduli. It is shown that the rank of the Yukawa matrix can decrease at specific loci in complex structure moduli space. In particular, we compute the up Yukawa coupling and the singlet-Higgs-lepton trilinear coupling in the heterotic standard model described in arXiv:1404.2767
hep-th↗
Yukawa Unification in Heterotic String Theory
We analyze Yukawa unification in the the context of $E_8\times E_8$ heterotic Calabi-Yau models which rely on breaking to a GUT theory via a non-flat gauge bundle and subsequent Wilson line breaking to the standard model. Our focus is on underlying GUT theories with gauge group $SU(5)$ or $SO(10)$. We provide a detailed analysis of the fact that, in contrast to traditional field theory GUTs, the underlying GUT symmetry of these models does not enforce Yukawa unification. Using this formalism, we present various scenarios where Yukawa unification can occur as a consequence of additional symmetries. These additional symmetries arise naturally in some heterotic constructions and we present an explicit heterotic line bundle model which realizes one of these scenarios.
hep-th↗
Superconformal field theory in three dimensions: Correlation functions of conserved currents
For N-extended superconformal field theories in three spacetime dimensions (3D), with N=1,2,3, we compute the two- and three-point correlation functions of the supercurrent and the flavour current multiplets. We demonstrate that supersymmetry imposes additional restrictions on the correlators of conserved currents as compared with the non-supersymmetric case studied by Osborn and Petkou in hep-th/9307010. It is shown that the three-point function of the supercurrent is determined by a single functional form consistent with the conservation equation and all the symmetry properties. Similarly, the three-point function of the flavour current multiplets is also determined by a single functional form in the N=1 and N=3 cases. The specific feature of the N=2 case is that two independent structures are allowed for the three-point function of flavour current multiplets, but only one of them contributes to the three-point function of the conserved currents contained in these multiplets. Since the supergravity and super-Yang-Mills Ward identities are expected to relate the coefficients of the two- and three-point functions under consideration, the results obtained for 3D superconformal field theory are analogous to those in 2D conformal field theory. In addition, we present a new supertwistor construction for compactified Minkowski superspace. It is suitable for developing superconformal field theory on 3D spacetimes other than Minkowski space, such as S^1 x S^2 and its universal covering space R x S^2.
hep-th↗
Implications of N=4 superconformal symmetry in three spacetime dimensions
We study implications of N=4 superconformal symmetry in three dimensions, thus extending our earlier results in arXiv:1503.04961 devoted to the N=1,2,3 cases. We show that the three-point function of the supercurrent in N=4 superconformal field theories contains two linearly independent forms. However, only one of these structures contributes to the three-point function of the energy-momentum tensor and the other one is present in those N=4 superconformal theories which are not invariant under the mirror map. We point out that general N=4 superconformal field theories admit two inequivalent flavour current multiplets and show that the three-point function of each of them is determined by one tensor structure. As an example, we compute the two- and three-point functions of the conserved currents in N=4 superconformal models of free hypermultiplets. We also derive the universal relations between the coefficients appearing in the two- and three-point correlators of the supercurrent and flavour current multiplets in all superconformal theories with N=1,2,3,4 supersymmetry. Our derivation is based on the use of Ward identities in conjunction with superspace reduction techniques.
hep-th↗
A Heterotic QCD Axion
We show that a KSVZ axion with a decay constant in the phenomenologically allowed range can be obtained in certain $E_8\times E_8$ heterotic string models. These models have an enhanced symmetry locus in the moduli space, and a non-universal, Kahler moduli dependent Fayet-Iliopoulos term which vanishes at this locus. Close to this locus the Fayet-Iliopoulos term is small and can lead to an axion decay constant significantly lower than the string scale. In this way, the no-go arguments of Svrcek and Witten, which are based on a universal, dilaton-dependent Fayet-Iliopoulos term, can be avoided. The relevant axion originates from phases of bundle moduli which correspond to deformations away from the enhanced symmetry locus. We construct an explicit example, based on a heterotic line bundle standard model, with all the required ingredients.
hep-th↗
Non-generic Couplings in Supersymmetric Standard Models
We study two phases of a heterotic standard model, obtained from a Calabi-Yau compactification of the E8xE8 heterotic string, in the context of the associated four-dimensional effective theories. In the first phase we have a standard model gauge group, an MSSM spectrum, four additional U(1) symmetries and singlet fields. In the second phase, obtained from the first by continuing along the singlet directions, three of the additional U(1) symmetries are spontaneously broken and the remaining one is a B-L symmetry. In this second phase, dimension five operators inducing proton decay are consistent with all symmetries and as such, they are expected to be present. We show that, contrary to this expectation, these operators are forbidden due to the additional U(1) symmetries present in the first phase of the model. We emphasize that such 'unexpected' absences of operators, due to symmetry enhancement at specific loci in the moduli space, can be phenomenologically relevant and, in the present case, protect the model from fast proton decay.
hep-th↗
A Heterotic Standard Model with B-L Symmetry and a Stable Proton
We consider heterotic Calabi-Yau compactifications with S(U(4)xU(1)) background gauge fields. These models lead to gauge groups with an additional U(1) factor which, under certain conditions, can combine with hypercharge to a B-L symmetry. The associated gauge boson is automatically super-massive and, hence, does not constitute a phenomenological problem. We illustrate this class of compactifications with a model based on the monad construction, which leads to a supersymmetric standard model with three families of quarks and leptons, one pair of Higgs doublets, three right-handed neutrinos and no exotics charged under the standard model group. The presence of the B-L symmetry means that the model is safe from proton decay induced by dimension four operators. Due to the presence of a special locus in moduli space where the bundle structure group is Abelian and the low-energy symmetry enhances we can also show the absence of dimension five proton-decay inducing operators.
hep-th↗
The Moduli Space of Heterotic Line Bundle Models: a Case Study for the Tetra-Quadric
It has recently been realised that polystable, holomorphic sums of line bundles over smooth Calabi-Yau three-folds provide a fertile ground for heterotic model building. Large numbers of phenomenologically promising such models have been constructed for various classes of Calabi-Yau manifolds. In this paper we focus on a case study for the tetra-quadric - a Calabi-Yau hypersurface embedded in a product of four CP1 spaces. We address the question of finiteness of the class of consistent and physically viable line bundle models constructed on this manifold. Further, for a specific semi-realistic example, we explore the embedding of the line bundle sum into the larger moduli space of non-Abelian bundles, both by means of constructing specific polystable non-Abelian bundles and by turning on VEVs in the associated low-energy theory. In this context, we explore the fate of the Higgs doublets as we move in bundle moduli space. The non-Abelian compactifications thus constructed lead to SU(5) GUT models with an additional global B-L symmetry. The non-Abelian compactifications inherit many of the appealing phenomenological features of the Abelian model, such as the absence of dimension four and dimension five operators triggering fast proton decay.
hep-th↗
Energy-Spin Trajectories in AdS_5 x S^5 from Semiclassical Vertex Operators
We study the relation between vertex operators in AdS_5 x S^5 and classical spinning string solutions. In the limit of large quantum numbers the treatment of vertex operators becomes semiclassical. In this regime, a given vertex operator carrying a certain set of quantum numbers defines a singular solution. We show in a number of examples that this solution coincides with the classical string solution with the same quantum numbers but written in a different two-dimensional coordinate system. The marginality condition imposed on an operator yields a relation between the energy and the other quantum numbers which is shown to coincide with that of the corresponding classical string solution. We also argue that in some cases vertex operators in AdS_5 x S^5 cannot be given by expressions similar to the ones in flat space and a more involved consideration is required.
hep-th↗
Relativistic Conformal Magneto-Hydrodynamics from Holography
We use the AdS/CFT correspondence to study first-order relativistic viscous magneto-hydrodynamics of (2+1) dimensional conformal magnetic fluids. It is shown that the first order magneto-hydrodynamics constructed following Landau and Lifshitz from the positivity of the entropy production is inconsistent. We propose additional contributions to the entropy motivated dissipative current and, correspondingly, new dissipative transport coefficients. We use the strongly coupled M2-brane plasma in external magnetic field to show that the new magneto-hydrodynamics leads to self-consistent results in the shear and sound wave channels.
hep-th↗