arXiv subjects

Ergin Sezgin

Publications and source records attributed to Ergin Sezgin.

At least 37 records · Page 2Linked to original sources

arXiv2021

On supersymmetric E11 exceptional field theory

We construct an infinite system of non-linear duality equations, including fermions, that are invariant under global E11 and gauge invariant under generalised diffeomorphisms upon the imposition of a suitable section constraint. We use finite-dimensional fermionic representations of the R-symmetry E11 to describe the fermionic contributions to the duality equations. These duality equations reduce to the known equations of E8 exceptional field theory or eleven-dimensional supergravity for appropriate (partial) solutions of the section constraint. Of key importance in the construction is an indecomposable representation of E11 that entails extra non-dynamical fields beyond those predicted by E11 alone, generalising the known constrained p-forms of exceptional field theories. The construction hinges on the tensor hierarchy algebra extension of E11, both for the bosonic theory and its supersymmetric extension.

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arXiv2020

11D Supergravity on $AdS_4 \times S^7$ versus $AdS_7 \times S^4$

The maximally supersymmetric Freund-Rubin vacua for eleven dimensional supergravity, namely $AdS_4 \times S^7$ and $AdS_7 \times S^4$, admit an analytic continuation to $S^4 \times S^7$. From the full harmonic expansions on $S^4 \times S^7$, it is shown that by analytical continuation to either $AdS_4$, or to $AdS_7$, the detailed structure of the Kaluza-Klein spectrum can be obtained for both vacua in a unified manner. The results are shown to be related by a simple rule which interchanges the spacetime and internal space representations. We also obtain the linearized field equations for the singletons and doubletons but they can be gauged away by fixing certain Stuckelberg shift symmetries inherited from the Kaluza-Klein reduction.

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arXiv2020

On the consistency of a class of R-symmetry gauged 6D N=(1,0) supergravities

R-symmetry gauged 6D (1,0) supergravities free from all local anomalies, with gauge groups $G\times G_R$ where $G_R$ is the R-symmetry group and $G$ is semisimple with rank greater than one, and which have no hypermultiplet singlets, are extremely rare. There are three such models known in which the gauge symmetry group is $G_1\times G_2 \times U(1)_R$ where the first two factors are $ \left(E_6/{\mathbb{Z}_3}\right) \times E_7$, $ G_2 \times E_7 $ and $F_4 \times Sp(9)$. These are models with single tensor multiplet, and hyperfermions in the $(1,912)$, $(14,56)$ and $(52,18)$ dimensional representations of $G_1\times G_2$, respectively. So far it is not known if these models follow from string theory. We highlight key properties of these theories, and examine constraints which may arise from the consistency of the quantization of anomaly coefficients formulated in their strongest form by Monnier and Moore. Assuming that the gauged models accommodate dyonic string excitations, we find that these constraints are satisfied only by the model with the $F_4 \times Sp(9)\times U(1)_R$ symmetry. We also discuss aspects of dyonic strings and potential caveats they may pose in applying the stated consistency conditions to the $R$-symmetry gauged models.

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arXiv2020

On one loop corrections in higher spin gravity

We propose an approach to compute one-loop corrections to the four-point amplitude in the higher spin gravities that are holographically dual to free $O(N)$, $U(N)$ and $USp(N)$ vector models. We compute the double-particle cut of one-loop diagrams by expressing them in terms of tree level four-point amplitudes. We then discuss how the remaining contributions to the complete one-loop diagram can be computed. With certain assumptions we find nontrivial evidence for the shift in the identification of the bulk coupling constant and $1/N$ in accordance with the previously established result for the vacuum energy.

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arXiv2018

E$_{7(7)}$ Exceptional Field Theory in Superspace

We formulate the locally supersymmetric E$_{7(7)}$ exceptional field theory in a $(4+56|32)$ dimensional superspace, corresponding to a 4D $N\!=\!8$ "external" superspace augmented with an "internal" 56-dimensional space. This entails the unification of external diffeomorphisms and local supersymmetry transformations into superdiffeomorphisms. The solutions to the superspace Bianchi identities lead to on-shell duality equations for the $p$-form field strengths for $p\leq 4$. The reduction to component fields provides a complete description of the on-shell supersymmetric theory. As an application of our results, we perform a generalized Scherk-Schwarz reduction and obtain the superspace formulation of maximal gauged supergravity in four dimensions parametrized by an embedding tensor.

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arXiv2017

On Exact Solutions and Perturbative Schemes in Higher Spin Theory

We review various methods for finding exact solutions of higher spin theory in four dimensions, and survey the known exact solutions of (non)minimal Vasiliev's equations. These include instanton-like and black hole-like solutions in (A)dS and Kleinian spacetimes. A perturbative construction of solutions with the symmetries of a domain wall is described as well. Furthermore, we review two proposed perturbative schemes: one based on perturbative treatment of the twistor space field equations followed by inverting Fronsdal kinetic terms using standard Green's functions; and an alternative scheme based on solving the twistor space field equations exactly followed by introducing the spacetime dependence using perturbatively defined gauge functions. Motivated by the need to provide a higher spin invariant characterization of the exact solutions, aspects of a proposal for a geometric description of Vasiliev's equation involving an infinite dimensional generalization of anti de Sitter space is revisited and improved.

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arXiv2017

Chern-Simons Matter Theories and Higher Spin Gravity

We compute the parity violating three point amplitudes with one scalar leg in higher spin gravity and compare results with those of Chern-Simons matter theories. The three-point correlators of the free boson, free fermion, critical vector model and Gross-Neveu model are reproduced including the dependence on the Chern-Simons coupling. We also perform a simple test of the modified higher spin equations proposed in arXiv:1605.02662 [hep-th] and find that the results are consistent with the AdS/CFT correspondence.

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arXiv2017

Beyond E11

We study the non-linear realisation of E11 originally proposed by West with particular emphasis on the issue of linearised gauge invariance. Our analysis shows even at low levels that the conjectured equations can only be invariant under local gauge transformations if a certain section condition that has appeared in a different context in the E11 literature is satisfied. This section condition also generalises the one known from exceptional field theory. Even with the section condition, the E11 duality equation for gravity is known to miss the trace component of the spin connection. We propose an extended scheme based on an infinite-dimensional Lie superalgebra, called the tensor hierarchy algebra, that incorporates the section condition and resolves the above issue. The tensor hierarchy algebra defines a generalised differential complex, which provides a systematic description of gauge invariance and Bianchi identities. It furthermore provides an E11 representation for the field strengths, for which we define a twisted first order self-duality equation underlying the dynamics.

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arXiv2016

One Loop Tests of Supersymmetric Higher Spin $AdS_4/CFT_3$

We compute one loop free energy for D=4 Vasiliev higher spin gravities based on Konstein-Vasiliev algebras hu(m;n|4), ho(m;n|4) or husp(m;n|4) and subject to higher spin preserving boundary conditions, which are conjectured to be dual to the U(N), O(N) or USp(N) singlet sectors, respectively, of free CFTs on the boundary of $AdS_4$. Ordinary supersymmetric higher spin theories appear as special cases of Konstein-Vasiliev theories, when the corresponding higher spin algebra contains $OSp({\cal N}|4)$ as subalgebra. In $AdS_4$ with $S^3$ boundary, we use a modified spectral zeta function method, which avoids the ambiguity arising from summing over infinite number of spins. We find that the contribution of the infinite tower of bulk fermions vanishes. As a result, the free energy is the sum of those which arise in type A and type B models with internal symmetries, the known mismatch between the bulk and boundary free energies for type B model persists, and ordinary supersymmetric higher spin theories exhibit the mismatch as well. The only models that have a match are type A models with internal symmetries, corresponding to $n=0$. The matching requires identification of the inverse Newton's constant $G_N^{-1}$ with $N$ plus a proper integer as was found previously for special cases. In $AdS_4$ with $S^1\times S^2$ boundary, the bulk one loop free energies match those of the dual free CFTs for arbitrary $m$ and $n$. We also show that a supersymmetric double-trace deformation of free CFT based on OSp(1|4) does not contribute to the ${\cal O}(N^0)$ free energy, as expected from the bulk.

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arXiv2016

Frobenius-Chern-Simons gauge theory

Given a set of differential forms on an odd-dimensional noncommutative manifold valued in an internal associative algebra H, we show that the most general cubic covariant Hamiltonian action, without mass terms, is controlled by an Z_2-graded associative algebra F with a graded symmetric nondegenerate bilinear form. The resulting class of models provide a natural generalization of the Frobenius-Chern-Simons model (FCS) that was proposed in arXiv:1505.04957 as an off-shell formulation of the minimal bosonic four-dimensional higher spin gravity theory. If F is unital and the Z_2-grading is induced from a Klein operator that is outer to a proper Frobenius subalgebra, then the action can be written on a form akin to topological open string field theory in terms of a superconnection valued in the direct product of H and F. We give a new model of this type based on a twisting of C[Z_2 x Z_4], which leads to self-dual complexified gauge fields on AdS_4. If F is 3-graded, the FCS model can be truncated consistently as to zero-form constraints on-shell. Two examples thereof are a twisting of C[(Z_2)^3] that yields the original model, and the Clifford algebra Cl_2n which provides an FCS formulation of the bosonic Konstein--Vasiliev model with gauge algebra hu(4^{n-1},0).

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arXiv2016

4D Higher Spin Gravity with Dynamical Two-Form as a Frobenius--Chern--Simons Gauge Theory

We provide an off-shell formulation of four-dimensional higher spin gravity based on a covariant Hamiltonian action on an open nine-dimensional Poisson manifold whose boundary consists of the direct product of spacetime and a noncommutative twistor space of S^2 x S^2 topology. The fundamental field is a superconnection consisting of even and odd differential forms valued in the odd and even sectors of a 3-graded associative algebra given by the direct product of an eight-dimensional Frobenius algebra and a higher spin algebra extended by inner Klein operators. The superconnection consists of two one-forms gauging the one-sided actions of the higher spin algebra, two bi-fundamental real forms given by the Weyl zero-form and a new dynamical two-form, an additional set of forms providing a maximal duality extension, and, finally, the Lagrange multipliers required for the covariant Hamiltonian action. In a particular two-form background, the model yields Vasiliev's recently proposed extended higher spin gravity equations, whose interaction terms are accounted for by de Rham closed globally defined forms arising in the dynamical two-form.

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arXiv2016

Action principles for higher and fractional spin gravities

We review various off-shell formulations for interacting higher-spin systems in dimensions 3 and 4. Associated with higher-spin systems in spacetime dimension 4 is a Chern-Simons action for a superconnection taking its values in a direct product of an infinite-dimensional algebra of oscillators and a Frobenius algebra. A crucial ingredient of the model is that it elevates the rigid closed and central two-form of Vasiliev's theory to a dynamical 2-form and doubles the higher-spin algebra, thereby considerably reducing the number of possible higher spin invariants and giving a nonzero effective functional on-shell. The two action principles we give for higher-spin systems in 3D are based on Chern-Simons and BF models. In the first case, the theory we give unifies higher-spin gauge fields with fractional-spin fields and an internal sector. In particular, Newton's constant is related to the coupling constant of the internal sector. In the second case, the BF action we review gives the fully nonlinear Prokushkin-Vasiliev, bosonic equations for matter-coupled higher spins in 3D. We present the truncation to a single, real matter field relevant in the Gaberdiel-Gopakumar holographic duality. The link between the various actions we present is the fact that they all borrow ingredients from Topological Field Theory. It has bee conjectured that there is an underlying and unifying 2-dimensional first-quantised description of the previous higher-spin models in 3D and 4D, in the form of a Cattaneo-Felder-like topological action containing fermionic fields.

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arXiv2016

New Unfolded Higher Spin Systems in $AdS_3$

We investigate the unfolded formulation of bosonic Lorentz tensor fields of arbitrary spin in $AdS_3$ containing a parity breaking mass parameter. They include deformations of the linearisations of the Prokushkin--Vasiliev higher spin theory around its critical points. They also provide unfolded formulations of linearized topologically massive higher spin fields including their critical versions. The gauge invariant degrees of freedom are captured by infinite towers of zero forms. We also introduce two inequivalent sets of gauge potentials given by trace constrained Fronsdal fields and trace unconstrained metric-like fields.

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arXiv2016

An Action for Matter Coupled Higher Spin Gravity in Three Dimensions

We propose a covariant Hamiltonian action for the Prokushkin and Vasiliev's matter coupled higher spin gravity in three dimensions. The action is formulated on ${\cal X}_4 \times {\cal Z}_2$ where ${\cal X}_4$ is an open manifold whose boundary contains spacetime and ${\cal Z}_2$ is a noncommutative twistor space. We examine various consistent truncations to models of BF type in ${\cal X}_4$ and ${\cal Z}_2$ with B$^2$ terms and central elements. They are obtained by integrating out the matter fields in the presence of a vacuum expectation value $ν\in \mathbb{R}$ for the zero-form master field. For $ν=0$, we obtain a model on ${\cal X}_4$ containing Blencowe's action and a model on ${\cal Z}_2$ containing the Prokushkin--Segal--Vasiliev action. For generic $ν$ (including $ν=0$), we propose an alternative model on ${\cal X}_4$ with gauge fields in the Weyl algebra of Wigner's deformed oscillator algebra and Lagrange multipliers in the algebra of operators acting in the Fock representation space of the deformed oscillators.

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arXiv2015

Massive N=2 Supergravity in Three Dimensions

There exists two distinct off-shell ${\mathcal{N}}=2$ supergravities in three dimensions. They are also referred to as ${\mathcal{N}}=(1,1)$ and ${\mathcal{N}}=(2,0)$ supergravities, and they arise from the coupling of the Weyl multiplet to a compensating scalar or vector multiplet, respectively, followed by fixing of conformal symmetries. The ${\mathcal{N}} =(p,q)$ terminology refers to the underlying anti-de Sitter superalgebras $OSp(2,p) \oplus OSp(2,q)$ with $R$-symmetry group $SO(p) \times SO(q)$. We construct off-shell invariants of these theories up to fourth order in derivatives. As an application of these results, we determine the special combinations of the ${\mathcal{N}}=(1,1)$ invariants that admit anti-de Sitter vacuum solution about which there is a ghost-free massive spin-2 multiplet of propagating modes. We also show that the ${\mathcal{N}}=(2,0)$ invariants do not allow such possibility.

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arXiv2014

Supersymmetric Warped AdS in Extended Topologically Massive Supergravity

We determine the most general form of off-shell N=(1,1) supergravity field configurations in three dimensions by requiring that at least one off-shell Killing spinor exists. We then impose the field equations of the topologically massive off-shell supergravity and find a class of solutions whose properties crucially depend on the norm of the auxiliary vector field. These are spacelike-squashed and timelike-stretched AdS_3 for the spacelike and timelike norms, respectively. At the transition point where the norm vanishes, the solution is null warped AdS_3. This occurs when the coefficient of the Lorentz-Chern-Simons term is related to the AdS radius by $μ\ell=2$. We find that the spacelike-squashed AdS_3 can be modded out by a suitable discrete subgroup of the isometry group, yielding an extremal black hole solution which avoid closed timelike curves.

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arXiv2013

Newton-Cartan Supergravity

We construct a supersymmetric extension of three-dimensional Newton-Cartan gravity by gauging a super-Bargmann algebra. In order to obtain a non-trivial supersymmetric extension of the Bargmann algebra one needs at least two supersymmetries leading to a N=2 super-Bargmann algebra. Due to the fact that there is a universal Newtonian time, only one of the two supersymmetries can be gauged. The other supersymmetry is realized as a fermionic Stueckelberg symmetry and only survives as a global supersymmetry. We explicitly show how, in the frame of a Galilean observer, the system reduces to a supersymmetric extension of the Newton potential. The corresponding supersymmetry rules can only be defined, provided we also introduce a `dual Newton potential'. We comment on the four-dimensional case.

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arXiv2012

Six-dimensional superconformal couplings of non-abelian tensor and hypermultiplets

We construct six-dimensional superconformal models with non-abelian tensor and hypermultiplets. They describe the field content of (2,0) theories, coupled to (1,0) vector multiplets. The latter are part of the non-abelian gauge structure that also includes non-dynamical three- and four-forms. The hypermultiplets are described by gauged nonlinear sigma models with a hyper-Kaehler cone target space. We also address the question of constraints in these models and show that their resolution requires the inclusion of abelian factors. These provide couplings that were previously considered for anomaly cancellations with abelian tensor multiplets and resulted in the selection of ADE gauge groups.

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