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Imtak Jeon

Publications and source records attributed to Imtak Jeon.

At least 19 recordsLinked to original sources
arXiv2026

Localisation of $\mathcal{N} = (2,2)$ theories on spindles of both twists

We consider two-dimensional $\mathcal{N}=(2,2)$ supersymmetric field theories living on a spindle $\mathbb{WCP}_{[n_1,n_2]}^1$. Starting from the spindle solutions of five-dimensional STU gauged supergravity, we construct theories on a spindle which preserve supersymmetry via either the twist or anti-twist mechanism and admit two Killing spinors of opposite R-charge. While the study of field theories on anti-twisted spindles has already been undertaken in some detail, the advantage of our approach allows for the derivation of analogous results in the twist case. We apply the technique of supersymmetric localisation to compute the exact partition function for a theory consisting of an abelian vector multiplet and a charged chiral multiplet in the presence of a Fayet-Iliopoulos term. We compare and contrast the results for the twisted and anti-twisted spindle and find a general formula which encompasses the partition function for both cases simultaneously.

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arXiv2026

Moduli-dependent one-loop entropy of hyperbolic BPS black hole in AdS$_4$

We study one-loop logarithmic corrections to the entropy of static hyperbolic BPS black holes in asymptotically AdS$_4$ spacetime. Our analysis is carried out in a consistent real-scalar truncation of ${\cal N}=2$ Fayet-Iliopoulos gauged supergravity specified by the prepotential $F=-i X^0 X^1$, which corresponds to an Einstein-Dilaton-Maxwell theory with a nontrivial scalar potential. In this model, the classical BPS attractor mechanism exhibits flat directions, leaving scalar moduli on the black hole horizon unfixed, while the Bekenstein-Hawking entropy depends only on the charges. We show that the resulting one-loop correction to the black hole entropy acquires a nontrivial dependence on the horizon moduli and induces an effective quantum potential that dynamically stabilizes them at a preferred value. Our results provide an explicit and concrete realization of quantum lifting of classical attractor flat directions in gauged supergravity.

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arXiv2025

Supersymmetric localisation of $\mathcal{N}=(2,2)$ theories on a spindle

We consider two-dimensional $\mathcal{N}=(2,2)$ supersymmetric field theories living on a weighted projective space $\mathbb{WCP}_{[n_1,n_2]}^1$, often referred to as a spindle. Starting from the spindle solution of five-dimensional minimal gauged supergravity, we construct a theory on a spindle which preserves supersymmetry via the anti-twist mechanism and admits two Killing spinors of opposite $R$-charge. We apply the technique of supersymmetric localisation to compute the exact partition function for a theory consisting of an abelian vector multiplet and a chiral multiplet, finding that the path integral localises to a real moduli space of vector multiplet fluctuations. We compute the one-loop determinants via the equivariant index, using both the method of unpaired eigenvalues and the fixed point theorem, finding agreement between the two approaches. We conclude with the explicit partition function for an example of a charged chiral multiplet in the presence of a Fayet-Iliopoulos term and comment on its dependence on the overall length scale of the geometry. This work paves the way towards uncovering two-dimensional dualities, such as mirror symmetry, for field theories defined on orbifold backgrounds.

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arXiv2024

Stability and topological nature of charged Gauss-Bonnet AdS black holes in five dimensions

We investigate the thermodynamics of Reissner-Nordstrom Gauss-Bonnet (RN-GB) black holes in anti-de Sitter (AdS) space with three horizon geometries (k=+1,0,-1) within the grand canonical ensemble. Using the recently developed topological approach to black hole thermodynamics, inspired by Duan's $\phi$-mapping theory, we analyze the black holes by treating both critical points in the phase diagram and black hole solutions as defects in the thermodynamic parameter space. Our results show that the Gauss-Bonnet coupling significantly alters the topological classification of RN-GB AdS black holes, distinguishing them from their RN AdS counterparts in the grand canonical ensemble, while aligning with their canonical ensemble counterparts. Complementary analyses of local stability using specific heat validate the implication of topological analysis. Furthermore, an evaluation of global stability via Gibbs free energy provides a comprehensive understanding on the system's phase structure. Notably, for k=+1, topological analysis suggests liquid-gas type phase transitions, whereas global analysis favors Hawking-Page transitions. For k=-1, topology indicates a single stable black hole branch, yet the global analysis reveals the presence of Hawking-Page transition.

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arXiv2024

Supersymmetric spectrum for vector multiplet on Euclidean AdS$_2$

Quantum study of supersymmetric theories on Euclidean two dimensional anti-de Sitter space (EAdS$_2$) requires complexified spectrum. For a chiral multiplet, we showed that the spectrum of the Dirac operator acquires a universal shift of $\text{i}/2$ from the real spectrum to make the supersymmetry between boson and fermion manifest, where both the bosonic and fermionic eigenfunctions are normalizable using an appropriate definition of Euclidean inner product. We extend this analysis to the vector multiplet, where we show that the gaugino requires both $+\text{i}/2$ and $-\text{i}/2$ shift from the real spectrum, and there is additional isolated point at vanishing spectral parameter which is mapped by supersymmetry to the boundary zero modes of the vector field. Furthermore, this spectral analysis shows that not every bosonic fields in the vector multiplet can satisfy normalizable boundary condition. Nevertheless, aided by a reorganization of fields into a cohomological form, we find the supersymmetry mapping between bosons and fermions in terms of the expansion coefficients with respect to the newly constructed basis.

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arXiv2023

Supersymmetry and complexified spectrum on Euclidean AdS$_2$

Quantum study of supersymmetric theories on Euclidean two dimensional anti-de Sitter space (AdS$_2$) is invalid if we use the standard normalizable functional basis due to its incompatibility with supersymmetry. We cure this problem by demonstrating that supersymmetry requires complexified spectrum and constructing the supersymmetric basis for scalar and spinor fields. Our new basis is free of fermionic zero modes, delta-function normalizable with respect to a newly defined inner product, and compatible with the supersymmetric asymptotic boundary condition. We also explore the one-loop evaluation using this basis and show that it agrees with the standard nonsupersymmetric basis up to a global contribution arising from the fermion zero mode.

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arXiv2023

Supersymmetric localization: ${\cal N}=(2,2)$ theories on S$^2$ and AdS$_2$

Application of the supersymmetric localization method to theories on anti-de Sitter spacetime has received recent interest, yet still remains as a challenging problem. In this paper, we focus on (global) Euclidean AdS$_2$, on which we consider an Abelian ${\cal N}=(2,2)$ theory and implement localization computation to obtain the exact partition function. For comparison, we also revisit the theory on S$^2$ and perform a parallel computation. We refine the notion of equivariant supersymmetry and use appropriate functional integration measure. For AdS$_2$ we choose a supersymmetric boundary condition which is compatible with the principle of variation. To evaluate the 1-loop determinant about the localization saddle, we use index theory and fixed point formula, where we pay attention to the effect of zero modes and their superpartners. The existence of fermionic superpartner of 1-form boundary zero modes is proven. Obtaining the 1-loop determinant requires expansion of the index that presents an ambiguity, which we resolve using boundary condition. The resulting partition function reveals an overall dependence on the size of the background manifold, AdS$_2$ as well as S$^2$, as a sum of two types of contributions: a local one from local conformal anomaly through the index computation and a global one coming from zero modes. This overall size dependence is confirmed by the perturbative 1-loop evaluation using heat kernel method.

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arXiv2023

Localization on $AdS_3 \times S^2$ I: the 4d/5d connection in off-shell Euclidean supergravity

We begin to develop the formalism of localization for the functional integral of supergravity on $AdS_3 \times S^2$. We show how the condition of supersymmetry in the Euclidean $\mathbb{H}^3/\mathbb{Z} \times S^2$ geometry naturally leads to a twist of the S$^2$ around the time direction of $AdS_3$. The twist gives us a five-dimensional Euclidean supergravity background dual to the elliptic genus of $(0,4)$ SCFT$_2$ at the semiclassical level. On this background we set up the off-shell BPS equations for one of the Killing spinors, such that the functional integral of five-dimensional Euclidean supergravity on $\mathbb{H}^3/\mathbb{Z} \times S^2$ localizes to its space of solutions. We obtain a class of solutions to these equations by lifting known off-shell BPS solutions of 4-dimensional supergravity on $AdS_2 \times S^2$. In order to do this consistently, we construct and use a Euclidean version of the off-shell 4d/5d lift of arxiv:1112.5371, which could be of independent interest.

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arXiv2022

Twisting and localization in supergravity: equivariant cohomology of BPS black holes

We develop the formalism of supersymmetric localization in supergravity using the deformed BRST algebra defined in the presence of a supersymmetric background as recently formulated in arxiv:1806.03690. The gravitational functional integral localizes onto the cohomology of a global supercharge $Q_\text{eq}$, obeying $Q_\text{eq}^2=H$, where $H$ is a global symmetry of the background. Our construction naturally produces a twisted version of supergravity whenever supersymmetry can be realized off-shell. We present the details of the twisted graviton multiplet and ghost fields for the superconformal formulation of four-dimensional N=2 supergravity. As an application of our formalism, we systematize the computation of the exact quantum entropy of supersymmetric black holes. In particular, we compute the one-loop determinant of the $Q_\text{eq} \mathcal{V}$ deformation operator for the off-shell fluctuations of the Weyl multiplet around the $AdS_2 \times S^2$ saddle. This result, which is consistent with the corresponding large-charge on-shell analysis, is needed to complete the first-principles computation of the quantum entropy.

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arXiv2020

Duality and Transport for Supersymmetric Graphene from the Hemisphere Partition Function

We use localization to compute the partition function of a four dimensional, supersymmetric, abelian gauge theory on a hemisphere coupled to charged matter on the boundary. Our theory has eight real supercharges in the bulk of which four are broken by the presence of the boundary. The main result is that the partition function is identical to that of ${\mathcal N}=2$ abelian Chern-Simons theory on a three-sphere coupled to chiral multiplets, but where the quantized Chern-Simons level is replaced by an arbitrary complexified gauge coupling $τ$. The localization reduces the path integral to a single ordinary integral over a real variable. This integral in turn allows us to calculate the scaling dimensions of certain protected operators and two-point functions of abelian symmetry currents at arbitrary values of $τ$. Because the underlying theory has conformal symmetry, the current two-point functions tell us the zero temperature conductivity of the Lorentzian versions of these theories at any value of the coupling. We comment on S-dualities which relate different theories of supersymmetric graphene. We identify a couple of self-dual theories for which the complexified conductivity associated to the U(1) gauge symmetry is $τ/2$.

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arXiv2015

Supersymmetric Localization for BPS Black Hole Entropy: 1-loop Partition Function from Vector Multiplets

We use the techniques of supersymmetric localization to compute the BPS black hole entropy in N=2 supergravity. We focus on the n_v+1 vector multiplets on the black hole near horizon background which is AdS_2 x S^2 space. We find the localizing saddle point of the vector multiplets by solving the localization equations, and compute the exact one loop partition function on the saddle point. Furthermore, we propose the appropriate functional integration measure. Through this measure, the one loop determinant is written in terms of the radius of the physical metric, which depends on the localizing saddle point value of the vector multiplets. The result for the one loop determinant is consistent with the logarithmic corrections to the BPS black hole entropy from vector multiplets.

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arXiv2015

Supersymmetric gauged Double Field Theory: Systematic derivation by virtue of \textit{Twist}

In a completely systematic and geometric way, we derive maximal and half-maximal supersymmetric gauged double field theories in lower than ten dimensions. To this end, we apply a simple twisting ansatz to the $D=10$ ungauged maximal and half-maximal supersymmetric double field theories constructed previously within the so-called semi-covariant formalism. The twisting ansatz may not satisfy the section condition. Nonetheless, all the features of the semi-covariant formalism, including its complete covariantizability, are still valid after the twist under alternative consistency conditions. The twist allows gaugings as supersymmetry preserving deformations of the $D=10$ untwisted theories after Scherk-Schwarz-type dimensional reductions. The maximal supersymmetric twist requires an extra condition to ensure both the Ramond-Ramond gauge symmetry and the $32$ supersymmetries unbroken.

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arXiv2013

Stringy Unification of Type IIA and IIB Supergravities under N=2 D=10 Supersymmetric Double Field Theory

To the full order in fermions, we construct D=10 type II supersymmetric double field theory. We spell the precise N=2 supersymmetry transformation rules as for 32 supercharges. The constructed action unifies type IIA and IIB supergravities in a manifestly covariant manner with respect to O(10,10) T-duality and a pair of local Lorentz groups, or Spin(1,9) \times Spin(9,1), besides the usual general covariance of supergravities or the generalized diffeomorphism. While the theory is unique, the solutions are twofold. Type IIA and IIB supergravities are identified as two different types of solutions rather than two different theories.

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arXiv2012

Periodic Arrays of M2-Branes

We consider periodic arrays of M2-branes in the ABJM model in the spirit of a circle compactification to D2-branes in type IIA string theory. The result is a curious formulation of three-dimensional maximally supersymmetric Yang-Mills theory in terms of fermions, seven transverse scalars, a non-dynamical gauge field and an additional scalar `dual gluon'. Upon further T-duality on a transverse torus we obtain a non-manifest-Lorentz-invariant description of five-dimensional maximally supersymmetric Yang-Mills. Here the additional scalar field can be thought of as the components of a two-form along the torus. This action can be viewed as an M-theory description of M5-branes on ${\mathbb T}^3$.

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arXiv2012

Supersymmetric Double Field Theory: Stringy Reformulation of Supergravity

We construct a supersymmetric extension of double field theory that realizes the ten-dimensional Majorana-Weyl local supersymmetry. In terms of a stringy differential geometry we proposed earlier, our action consists of five simple terms -- two bosonic plus three fermionic -- and manifests not only diffeomorphism and one-form gauge symmetry of B-field, but also O(10,10) T-duality as well as a direct product of two local Lorentz symmetries, SO(1,9) \times SO(9,1). A gauge fixing that identifies the double local Lorentz groups reduces our action to the minimal supergravity in ten dimensions.

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arXiv2012

Ramond-Ramond Cohomology and O(D,D) T-duality

In the name of supersymmetric double field theory, superstring effective actions can be reformulated into simple forms. They feature a pair of vielbeins corresponding to the same spacetime metric, and hence enjoy double local Lorentz symmetries. In a manifestly covariant manner --with regard to O(D,D) T-duality, diffeomorphism, B-field gauge symmetry and the pair of local Lorentz symmetries-- we incorporate R-R potentials into double field theory. We take them as a single object which is in a bi-fundamental spinorial representation of the double Lorentz groups. We identify cohomological structure relevant to the field strength. A priori, the R-R sector as well as all the fermions are O(D,D) singlet. Yet, gauge fixing the two vielbeins equal to each other modifies the O(D,D) transformation rule to call for a compensating local Lorentz rotation, such that the R-R potential may turn into an O(D,D) spinor and T-duality can flip the chirality exchanging type IIA and IIB supergravities.

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arXiv2012

Incorporation of fermions into double field theory

Based on the stringy differential geometry we proposed earlier, we incorporate fermions such as gravitino and dilatino into double field theory in a manifestly covariant manner with regard to O(D,D) T-duality, diffeomorphism, one-form gauge symmetry for B-field and a pair of local Lorentz symmetries. We note that there are two kinds of fermions in double field theory: O(D,D) singlet and non-singlet which may be identified, respectively as the common and the non-common fermionic sectors in type IIA and IIB supergravities. For each kind, we construct corresponding covariant Dirac operators. Further, we derive a simple criterion for an O(D,D) rotation to flip the chirality of the O(D,D) non-singlet chiral fermions, which implies the exchange of type IIA and IIB supergravities.

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