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Ergin Sezgin

Publications and source records attributed to Ergin Sezgin.

At least 19 recordsLinked to original sources
arXiv2026

Diagonally gauged anomaly-free 6D supergravities and their vacua

We describe a bounded search for local and global anomaly-free six-dimensional $(1,0)$ models with tensor number $T=1$ and gauge group containing a diagonal abelian factor $U(1)_{R+}$. The abelian factor is the diagonal combination of the usual gauged $U(1)_R$ and a $U(1)\subset Sp(n_H)$ acting on hypermultiplets. We have searched for locally and globally anomaly-free $G_1\times U(1)_{R+}$ and $G_1\times G_2\times U(1)_{R+}$ models, subject to restrictions on the ranks of the simple factors and on the maximal charges carried by matter. We find that, unlike the case of $U(1)_R$ gauged models which are relatively rare, the diagonally gauged ones offer a rich landscape. We also study the 6D vacua of these models and find that they admit supersymmetric 6D Minkowski vacua, for which the diagonal nature of the R-symmetry gauging is necessary.

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arXiv2025

4D de Sitter from 6D gauged supergravity with Green-Schwarz counterterm

Taking into account the Green-Schwarz anomaly counterterm in R-symmetry gauged $N=(1,0)$ supergravity in six dimensions, and the associated modification in the Maxwell kinetic term and potential, the theory admits half-supersymmetric Mink$_4\times S^2$ and non-supersymmetric dS$_4 \times S^2$ solutions with or without a monopole on $S^2$. The monopole charge and the anomaly coefficients play key roles in the vacuum structure and a diagonal gauging in which an admixture of an external $U(1)$ with the R-symmetry $U(1)_R$ is needed for the de Sitter solutions to exist. We determine the full Kaluza-Klein spectrum for both vacua. The spectrum is unitary in the Minkowski case but in the case of de Sitter vacuum, the dilaton and the breathing mode are tachyonic. We show that turning on small perturbations of the tachyonic modes around dS$_4\times S^2$ with a monopole on $S^2$ triggers a flow evolving towards Mink$_4\times S^2$ with the minimal potential energy. The diagonally gauged model also supports dS$_2\times S^4$ solution which avoids tachyons for certain values of the flux on dS$_2$. We also find nonsupersymmetric (A)dS$_4\times S^2$ solutions, when we turn on a flux associated with external $U(1)$ gauge field only, and show that they support the phenomenon of scale separation under certain conditions on anomaly coefficients.

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arXiv2025

Massive spin 3 and Metric-Affine Gravity

Symmetric Metric-Affine Gravity is a theory of gravity with an independent non-metric connection, and zero torsion. It can be thought of as ordinary metric gravity coupled to a rank-three tensor Q, symmetric in one pair of indices. This field carries a spin-three degree of freedom. We find that, in contrast to the totally symmetric case, it is possible to arrange the parameters in the Lagrangian, so that, at the linearized level, the spin-three state, either alone or in combination with a spin-0 state, has a healthy propagation.

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arXiv2025

Global anomalies in $6D$ gauged supergravities

There exists a rare class of R-symmetry gauged $N=(1,0)$ supergravities in six dimensions with gauge group $G\times U(1)_R$, where $G$ is semisimple with rank greater than one, and the number of tensor multiplets $n_T=1$, which are free from all local anomalies. We find new members of this family, in which $G$ contains up to four factors. We study the global anomalies of these models in a framework in which the Dirac quantization of the anomaly coefficients and the well-definedness of the Green-Schwarz anomaly counterterm in generic backgrounds play key roles, and we apply the anomaly freedom criteria that takes this into account as formulated by Monnier and Moore in \cite{Monnier:2018nfs}. To this end we use the result derived by Yuji Tachikawa in the appendix which states that the spin cobordism group $\Omega_7^{\rm Spin}(BG)$ vanishes for $G=\sG_1\times \cdots \times \sG_n$ where $\sG_i$ is $U(1)$ or any simple simply-connected non-Abelian compact Lie group. We also require correct sign for the vector field kinetic terms, and positive Gauss-Bonnet term. We find that among the models considered here only one of them fails to satisfy all the stated criteria. We also find that, in general, the requirement that the anomaly coefficients defined by the factorized anomaly polynomial are elements of a unimodular charge lattice imposes a constraint on the number of vector multiplets given by $n_{V}=8\ {\rm mod}\ 12$ for $\Uni{1}_{R}$, and $n_{V} = 12$ or $96$ for $\Sp{1}_{R}$ gauged models.

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arXiv2025

Scale separation on AdS$_3\times S^3$ with and without supersymmetry

Six-dimensional chiral gauged Einstein-Maxwell supergravity admits a two-parameter rotating dyonic string solution whose near horizon limit is the direct product of AdS$_3$ and a squashed three-sphere $S^3$. For a particular relation between the two parameters, the solution preserves $1/2$ supersymmetry. We determine the complete Kaluza-Klein spectrum of the theory around these AdS$_3$ backgrounds. For the supersymmetric backgrounds, the states organize into infinite towers of long and short multiplets of OSp(2|2). In a certain limit of parameters, both the supersymmetric and the non-supersymmetric spectra exhibit scale separation. In the latter case there are five topologically massive vectors and five scalars retaining finite masses with integer conformal dimensions, and in the supersymmetric case there are supersymmetric partners with half integer conformal dimensions, while all other masses diverge.

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arXiv2025

A brief history of supermembranes

``When to the sessions of sweet silent thought I summon up re-membranes of things past, I sigh the lack of many a thing I sought''. (Apologies to William Shakespeare)

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arXiv2024

Singletons in supersymmetric field theories and in supergravity

We consider $N=1$ supergravity coupled to a Wess-Zumino multiplet with a potential such that the resulting AdS energies saturate the unitarity and Breitenlohner-Freedman bounds, respectively. Imposing regular boundary conditions that preserve supersymmetry and support finite norms, the spectrum forms an $OSp(1,4)$ supermultiplet in which the singleton representation is absent. We study the case in which this boundary condition is relaxed such that the singleton and its superpartners survive and form an indecomposable representation of $OSp(1,4)$. Focusing on the global limit of the model, we carry out its holographic renormalization, in which a singletonic action makes appearance in the boundary action.

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arXiv2024

Higher Derivative Supergravities in Diverse Dimensions

We survey on-shell and off-shell higher derivative supergravities in dimensions $1\le D\le 11$. Various approaches to their construction, including the Noether procedure, (harmonic) superspace, superform method, superconformal tensor calculus, $S$-matrix and dimensional reduction, are summarized. Primarily the bosonic parts of the invariants and the supertransformations of the fermionic fields are provided. The process of going on-shell, solutions to the Killing spinor equations, typical supersymmetric solutions, and the role of duality symmetries in the context of $R^4, D^4 R^4$ and $D^6 R^4$ invariants are reviewed.

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arXiv2023

Survey of supergravities

A large class of supergravities in diverse dimensions are surveyed. This includes maximal supergravities, their general gaugings in the framework of embedding tensor formalism, supergravities with less than maximal supersymmetry, their matter couplings and general gaugings. The emphasis is on summarizing their most general form to date, and primarily in their component formulation. A class of exceptional field theories in an extended geometric framework are summarized briefly. For most of the supergravities surveyed, the bosonic part of the Lagrangians and supertransformations up to leading terms in fermions are given.

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arXiv2023

New anomaly free supergravities in six dimensions

An extended search for anomaly free matter coupled $N=(1,0)$ supergravity in six dimension is carried out by two different methods which we refer to as the graphical and rank methods. In the graphical method the anomaly free models are built from single gauge group models, called nodes, which can only have gravitational anomalies. We search for anomaly free theories with gauge groups $G_1\times...\times G_n$ with $n=1,2,...$ (any number of factors) and $G_1\times...\times G_n \times U(1)_R$ where $n=1,2,3$ and $U(1)_R$ is the $R$-symmetry group. While we primarily consider models with the tensor multiplet number $n_T=1$, we also provide some results for $n_T\ne 1$ with an unconstrained number of charged hypermultiplets. We find a large number of ungauged anomaly free theories. However, in the case of $R$-symmetry gauged models with $n_T=1$, in addition to the three known anomaly free theories with $G_1\times G_2 \times U(1)_R$ type symmetry, we find only six new remarkably anomaly free models with symmetry groups of the form $G_1\times G_2\times G_3 \times U(1)_R$. In the case of $n_T=1$ and ungauged models, excluding low rank group factors and considering only low lying representations, we find all anomaly free theories. Remarkably, the number of group factors does not exceed four in this class. The proof of completeness in this case relies on a bound which we establish for a parameter characterizing the difference between the number of non-singlet hypermultiplets and the dimension of the gauge group.

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arXiv2023

Higher derivative couplings of hypermultiplets

We construct the four-derivative supersymmetric extension of $(1,0), 6D$ supergravity coupled to Yang-Mills and hypermultiplets. The hypermultiplet scalars are taken to parametrize the quaternionic projective space $Hp(n)=Sp(n,1)/Sp(n)\times Sp(1)_R$. The hyperscalar kinetic term is not deformed, and the quaternionic Kähler structure and symmetries of $Hp(n)$ are preserved. The result is a three parameter Lagrangian supersymmetric up to first order in these parameters. Considering the case of $Hp(1)$ we compare our result with that obtained from the compactification of $10D$ heterotic supergravity on four-torus, consistently truncated to $N=(1,0)$, in which the hyperscalars parametrize $SO(4,1)/SO(4)$. We find that depending on how $Sp(1) \subset Sp(1,1)$ is embedded in $SO(4)$, the results agree for a specific value of the parameter that governs the higher derivative hypermultiplet couplings.

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arXiv2023

Extended geometry of magical supergravities

We provide, through the framework of extended geometry, a geometrisation of the duality symmetries appearing in magical supergravities. A new ingredient is the general formulation of extended geometry with structure group of non-split real form. A simple diagrammatic rule for solving the section constraint by inspection of the Satake diagram is derived.

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arXiv2022

Dualization of Higher Derivative Heterotic Supergravities in $6D$ and $10D$

There exist two four-derivative extensions of $N=(1,0)$ supergravity in six dimensions. A particular combination of them is known to dualize to the analog of the the Bergshoeff-de Roo (BdR) action in $10D$. Here we first show that the two extensions are not related to each other by any field redefinitions. Next, we dualize them separately thereby obtaining a two parameter dual theory. This is done directly at the level of the action, thus avoiding the laborious method of integrating equations of motion of the dualized theory into an action. To explore whether a similar phenomenon exists in $10D$, we study the dualization of the BdR action in $10D$ in detail. We find an obstacle in the separation of the result into a sum of two independent invariants because of the presence of terms which do not lift from $6D$ to $10D$. We also compare the dual of the BdR action with an existing result obtained in superspace. We find that the bosonic actions agree modulo field redefinitions.

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arXiv2022

Snowmass White Paper: Higher Spin Gravity and Higher Spin Symmetry

Higher Spin Gravity refers to extensions of gravity including at least one field of spin greater than two. These extensions are expected to provide manageable models of quantum gravity thanks to the infinite-dimensional (higher spin) gauge symmetry constraining them. One of the key aspects of Higher Spin Gravity/Symmetry is the range and diversity of topics it embraces: (a) higher spin fields play a role in quantum gravity, AdS/CFT, string theory and are expected to have important consequences in cosmology and black hole physics; (b) higher spin symmetry finds applications in Conformal Field Theories, condensed matter systems and dualities therein; (c) these models often rely on tools developed in the study of the mathematical foundations of QFT or in pure mathematics: from deformation quantization and non-commutative geometry to conformal geometry, graded geometry (including BV-BRST quantization), and geometry of PDEs. Recent exciting applications also involve (d) modelling the coalescence of black hole binaries as scattering of massive higher spin particles.

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arXiv2021

Dimensional reduction of higher derivative heterotic supergravity

Higher derivative couplings of hypermultiplets to $6D, N=(1,0)$ supergravity are obtained from dimensional reduction of 10D heterotic supergravity that includes order $α'$ higher derivative corrections. Reduction on $T^4$ is followed by a consistent truncation. In the resulting action the hyperscalar fields parametrize the coset $SO(4,4)/(SO(4)\times SO(4))$. While the $SO(4,4)$ symmetry is ensured by Sen's construction based on string field theory, its emergence at the field theory level is a nontrivial phenomenon. A number of field redefinitions in the hypermultiplet sector are required to remove several terms that break the $SO(4)\times SO(4)$ down to its $SO(4)$ diagonal subgroup in the action and the supersymmetry transformation rules. Working with the Lorentz Chern-Simons term modified 3-form field strength, where the spin connection has the 3-form field strength as torsion, is shown to simplify considerably the dimensional reduction.

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arXiv2021

A master exceptional field theory

We construct a pseudo-Lagrangian that is invariant under rigid $E_{11}$ and transforms as a density under $E_{11}$ generalised diffeomorphisms. The gauge-invariance requires the use of a section condition studied in previous work on $E_{11}$ exceptional field theory and the inclusion of constrained fields that transform in an indecomposable $E_{11}$-representation together with the $E_{11}$ coset fields. We show that, in combination with gauge-invariant and $E_{11}$-invariant duality equations, this pseudo-Lagrangian reduces to the bosonic sector of non-linear eleven-dimensional supergravity for one choice of solution to the section condition. For another choice, we reobtain the $E_8$ exceptional field theory and conjecture that our pseudo-Lagrangian and duality equations produce all exceptional field theories with maximal supersymmetry in any dimension. We also describe how the theory entails non-linear equations for higher dual fields, including the dual graviton in eleven dimensions. Furthermore, we speculate on the relation to the $E_{10}$ sigma model.

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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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