Sung-Soo Kim

Bio: Sung-Soo Kim is an academic researcher from University of Electronic Science and Technology of China. The author has contributed to research in topics: Light cone & Superspace. The author has an hindex of 10, co-authored 22 publications receiving 252 citations. Previous affiliations of Sung-Soo Kim include Université libre de Bruxelles & University of Florida.

E7(7) on the light cone

Abstract: We use the Cremmer-Julia E-7(7) non-linear symmetry of N = 8 Supergravity to derive its order k(2) on-shell Hamiltonian in terms of one chiral light-cone superfield. By requiring that E-7(7) commute with the super-Poincare group, we deduce to lowest non-trivial order in k, the light cone E-7(7) transformations of all fields of the theory, including the gravition. We then derive the dynamical supersymmetry transformation to order k(2), and express the Hamiltonian as a quadratic form in the chiral superfield.

Extremal solutions of the S3 model and nilpotent orbits of G2(2)

Abstract: We study extremal black hole solutions of the S3 model (obtained by setting S=T=U in the STU model) using group theoretical methods Upon dimensional reduction over time, the S3 model exhibits the pseudo-Riemannian coset structure $ {{G} \left/ {{\tilde{K}}} \right} $ with G = G2(2) and $ \tilde{K} = {\text{S}}{{\text{O}}_0}\left( {2,2} \right) $ We study nilpotent $ \tilde{K} $ -orbits of G2(2) corresponding to non-rotating single-center extremal solutions We find six such distinct $ \tilde{K} $ -orbits Three of these orbits are supersymmetric, one is non-supersymmetric, and two are unphysical We write general solutions and discuss examples in all four physical orbits We show that all solutions in supersymmetric orbits when uplifted to five-dimensional minimal supergravity have single-center Gibbons-Hawking space as their four-dimensional Euclidean hyper-Kahler base space We construct hitherto unknown extremal (supersymmetric as well as non-supersymmetric) pressureless black strings of minimal five-dimensional supergravity and briefly discuss their relation to black rings

Bootstrapping BPS spectra of 5d/6d field theories

Abstract: We propose a systematic approach to computing the BPS spectrum of any 5d/6d supersymmetric quantum field theory in Coulomb phases, which admits either gauge theory descriptions or geometric descriptions, based on the Nakajima-Yoshioka’s blowup equations. We provide a significant generalization of the blowup equation approach in terms of both properly quantized magnetic fluxes on the blowup $$ \hat{\mathrm{\mathbb{C}}} $$ 2 and the effective prepotential for 5d/6d field theories on the Omega background which is uniquely determined by the Chern-Simons couplings on their Coulomb branches. We employ our method to compute BPS spectra of all rank-1 and rank-2 5d Kaluza-Klein (KK) theories descending from 6d $$ \mathcal{N} $$ = (1, 0) superconformal field theories (SCFTs) compactified on a circle with/without twist. We also discuss various 5d SCFTs and KK theories of higher ranks, which include a few exotic cases such as new rank-1 and rank-2 5d SCFTs engineered with frozen singularity as well as the 5d SU(3)8 gauge theory currently having neither a brane web nor a smooth shrinkable geometric description. The results serve as non-trivial checks for a large class of non-trivial dualities among 5d theories and also as independent evidences for the existence of certain exotic theories.

Counterterms in gravity in the light-front formulation and a D = 2 conformal-like symmetry in gravity

Abstract: In this paper we discuss gravity in the light-front formulation (light-cone gauge) and show how possible counterterms arise. We find that Poincare invariance is not enough to find the three-point counterterms uniquely. Higher-spin fields can intrude and mimic three-point higher derivative gravity terms. To select the correct term we have to use the remaining reparametrization invariance that exists after the gauge choice. We finally sketch how the corresponding programme for N = 8 Supergravity should work.

What is the simplest quantum field theory

Abstract: Conventional wisdom says that the simpler the Lagrangian of a theory the simpler its perturbation theory. An ever-increasing understanding of the structure of scattering amplitudes has however been pointing to the opposite conclusion. At tree level, the BCFW recursion relations that completely determine the S-matrix are valid not for scalar theories but for gauge theories and gravity, with gravitational amplitudes exhibiting the best UV behavior at infinite complex momentum. At 1-loop, amplitudes in $ \mathcal{N} = 4 $ SYM only have scalar box integrals, and it was recently conjectured that the same property holds for $ \mathcal{N} = 8 $ SUGRA, which plays an important role in the suspicion that this theory may be finite. In this paper we explore and extend the S-matrix paradigm, and suggest that $ \mathcal{N} = 8 $ SUGRA has the simplest scattering amplitudes in four dimensions. Labeling external states by supercharge eigenstates-Grassmann coherent states-allows the amplitudes to be exposed as completely smooth objects, with the action of SUSY manifest. We show that under the natural supersymmetric extension of the BCFW deformation of momenta, all tree amplitudes in $ \mathcal{N} = 4 $ SYM and $ \mathcal{N} = 8 $ SUGRA vanish at infinite complex momentum, and can therefore be determined by recursion relations. An important difference between $ \mathcal{N} = 8 $ SUGRA and $ \mathcal{N} = 4 $ SYM is that the massless S-matrix is defined everywhere on moduli space, and is acted on by a non-linearly realized E 7(7) symmetry. We elucidate how non-linearly realized symmetries are reflected in the more familiar setting of pion scattering amplitudes, and go on to identify the action of E 7(7) on amplitudes in $ \mathcal{N} = 8 $ SUGRA. Moving beyond tree level, we give a simple general discussion of the structure of 1-loop amplitudes in any QFT, in close parallel to recent work of Forde, showing that the coefficients of scalar “triangle” and “bubble” integrals are determined by the “pole at infinite momentum” of products of tree amplitudes appearing in cuts. In $ \mathcal{N} = 4 $ SYM and $ \mathcal{N} = 8 $ SUGRA, the on-shell superspace makes it easy to compute the multiplet sums that arise in these cuts by relating them to the best behaved tree amplitudes of highest spin, leading to a straightforward proof of the absence of triangles and bubbles at 1-loop. We also argue that rational terms are absent. This establishes that 1-loop amplitudes in $ \mathcal{N} = 8 $ SUGRA only have scalar box integrals. We give an explicit expression for 1-loop amplitudes for both $ \mathcal{N} = 4 $ SYM and $ \mathcal{N} = 8 $ SUGRA in terms of tree amplitudes that can be determined recursively. These amplitudes satisfy further relations in $ \mathcal{N} = 8 $ SUGRA that are absent in $ \mathcal{N} = 4 $ SYM. Since both tree and 1-loop amplitudes for maximally supersymmetric theories can be completely determined by their leading singularities, it is natural to conjecture that this property holds to all orders of perturbation theory. This is the nicest analytic structure amplitudes could possibly have, and if true, would directly imply the perturbative finiteness of $ \mathcal{N} = 8 $ SUGRA. All these remarkable properties of scattering amplitudes call for an explanation in terms of a “weak-weak” dual formulation of QFT, a holographic dual of flat space.

Asymptotic symmetries of Yang-Mills theory

Abstract: Asymptotic symmetries at future null infinity ( $$ \mathrm{\mathcal{I}} $$ +) of Minkowski space for electrodynamics with massless charged fields, as well as nonabelian gauge theories with gauge group G, are considered at the semiclassical level. The possibility of charge/color flux through $$ \mathrm{\mathcal{I}} $$ + suggests the symmetry group is infinite-dimensional. It is conjectured that the symmetries include a G Kac-Moody symmetry whose generators are “large” gauge transformations which approach locally holomorphic functions on the conformal two-sphere at $$ \mathrm{\mathcal{I}} $$ + and are invariant under null translations. The Kac-Moody currents are constructed from the gauge field at the future boundary of $$ \mathrm{\mathcal{I}} $$ +. The current Ward identities include Weinberg’s soft photon theorem and its colored extension.

M5-Branes, D4-Branes and Quantum 5D super-Yang-Mills

Abstract: We revisit the relation of the six-dimensional (2, 0) M5-brane Conformal Field Theory compactified on S1 to 5D maximally supersymmetric Yang-Mills Gauge Theory. We show that in the broken phase 5D super-Yang-Mills contains a spectrum of soliton states that can be identified with the complete Kaluza-Klein modes of an M2-brane ending on the M5-branes. This provides evidence that the (2, 0) theory on S1 is equivalent to 5D super-Yang-Mills with no additional UV degrees of freedom, suggesting that the latter is in fact a well-defined quantum theory and possibly finite.

The Kerr/CFT Correspondence and its Extensions

Abstract: We present a first-principles derivation of the main results of the Kerr/CFT correspondence and its extensions using only tools from gravity and quantum field theory, filling a few gaps in the literature when necessary. Firstly, we review properties of extremal black holes that imply, according to semi-classical quantization rules, that their near-horizon quantum states form a centrally-extended representation of the one-dimensional conformal group. This motivates the conjecture that the extremal Kerr and Reissner-Nordstrom black holes are dual to the chiral limit of a two-dimensional CFT. We also motivate the existence of an SL(2, ℤ) family of two-dimensional CFTs, which describe in their chiral limit the extremal Kerr-Newman black hole. We present generalizations in anti-de Sitter spacetime and discuss other matter-coupling and higher-derivative corrections. Secondly, we show how a near-chiral limit of these CFTs reproduces the dynamics of near-superradiant probes around near-extremal black holes in the semi-classical limit. Thirdly, we review how the hidden conformal symmetries of asymptotically-flat black holes away from extremality, combined with their properties at extremality, allow for a microscopic accounting of the entropy of non-extremal asymptotically-flat rotating or charged black holes. We conclude with a list of open problems.

n-ary algebras: a review with applications

Abstract: This paper reviews the properties and applications of certain n-ary generalizations of Lie algebras in a self-contained and unified way. These generalizations are algebraic structures in which the two entries Lie bracket has been replaced by a bracket with n entries. Each type of n-ary bracket satisfies a specific characteristic identity which plays the role of the Jacobi identity for Lie algebras. Particular attention will be paid to generalized Lie algebras, which are defined by even multibrackets obtained by antisymmetrizing the associative products of its n components and that satisfy the generalized Jacobi identity, and to Filippov (or n-Lie) algebras, which are defined by fully antisymmetric n-brackets that satisfy the Filippov identity. Three-Lie algebras have surfaced recently in multi-brane theory in the context of the Bagger-Lambert- Gustavsson model. Because of this, Filippov algebras will be discussed at length, including the cohomology complexes that govern their central extensions and their deformations (it turns out that Whitehead's lemma extends to all semisimple n-Lie algebras). When the skewsymmetry of the Lie or n-Lie algebra bracket is relaxed, one is led to a more general type of n-algebras, the n-Leibniz algebras. These will be discussed as well, since they underlie the cohomological properties of n-Lie algebras. The standard Poisson structure may also be extended to the n-ary case. We shall review here the even generalized Poisson structures, whose generalized Jacobi identity reproduces the pattern of the generalized Lie algebras, and the Nambu-Poisson structures, which satisfy the Filippov identity and determine Filippov algebras. Finally, the recent work of Bagger-Lambert and Gustavsson on superconformal Chern-Simons theory will be briefly discussed. Emphasis will be made on the appearance of the 3-Lie algebra structure and on why the A4 model may be formulated in terms of an ordinary Lie algebra, and on its Nambu bracket generalization.