arXiv subjects

Euihun Joung

Publications and source records attributed to Euihun Joung.

At least 37 records · Page 2Linked to original sources

arXiv2018

Character Integral Representation of Zeta function in AdS$_{d+1}$: II. Application to partially-massless higher-spin gravities

We compute the one-loop free energies of the type-A$_\ell$ and type-B$_\ell$ higher-spin gravities in $(d+1)$-dimensional anti-de Sitter (AdS$_{d+1}$) spacetime. For large $d$ and $\ell$, these theories have a complicated field content, and hence it is difficult to compute their zeta functions using the usual methods. Applying the character integral representation of zeta function developed in the companion paper arXiv:1805.05646 to these theories, we show how the computation of their zeta function can be shortened considerably. We find that the results previously obtained for the massless theories ($\ell=1$) generalize to their partially-massless counterparts (arbitrary $\ell$) in arbitrary dimensions.

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arXiv2018

Character Integral Representation of Zeta function in AdS$_{d+1}$: I. Derivation of the general formula

The zeta function of an arbitrary field in $(d+1)$-dimensional anti-de Sitter (AdS) spacetime is expressed as an integral transform of the corresponding $so(2,d)$ representation character, thereby extending the results of arXiv:1603.05387 for AdS$_4$ and AdS$_5$ to arbitrary dimensions. The integration in the variables associated with the $so(d)$ part of the character can be recast into a more explicit form using derivatives. The explicit derivative expressions are presented for AdS$_{d+1}$ with $d=2,3,4,5,6$.

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arXiv2018

Twisted Flato-Fronsdal Theorem for Higher-Spin Algebras

We explore the relation between the singleton and adjoint modules of higher-spin algebras via so(2,d) characters. In order to relate the tensor product of the singleton and its dual to the adjoint module, we consider a heuristic formula involving symmetrization over the variables of the character. We show that our formula reproduces correctly the adjoint-module character for type-A (and its high-order extensions) and type-B higher-spin gravity theories in any dimension. Implications and subtleties of this symmetrization prescription in other models are discussed.

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arXiv2018

Asymptotic Symmetries of Colored Gravity in Three Dimensions

Three-dimensional colored gravity refers to nonabelian isospin extension of Einstein gravity. We investigate the asymptotic symmetry algebra of the $SU(N)$-colored gravity in (2+1)-dimensional anti-de Sitter spacetime. Formulated by the Chern-Simons theory with $SU(N,N)\times SU(N,N)$ gauge group, the theory contains graviton, $SU(N)$ Chern-Simons gauge fields and massless spin-two multiplets in the $SU(N)$ adjoint representation, thus extending diffeomorphism to colored, nonabelian counterpart. We identify the asymptotic symmetry as Poisson algebra of generators associated with the residual global symmetries of the nonabelian diffeomorphism set by appropriately chosen boundary conditions. The resulting asymptotic symmetry algebra is a nonlinear extension of Virasoro algeba and $\widehat{\mathfrak{su}(N)}$ Kac-Moody algebra, supplemented by additional generators corresponding to the massless spin-two adjoint matter fields.

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arXiv2018

Non-Relativistic Limits of Colored Gravity in Three Dimensions

The three-dimensional non-relativistic isometry algebras, namely Galilei and Newton-Hooke algebras, are known to admit double central extensions, which allows for non-degenerate bilinear forms hence for action principles through Chern-Simons formulation. In three-dimensional colored gravity, the same central extension helps the theory evade the multi-graviton no-go theorems by enlarging the color-decorated isometry algebra. We investigate the non-relativistic limits of three-dimensional colored gravity in terms of generalized İnönü-Wigner contractions.

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arXiv2017

Exploring Free Matrix CFT Holographies at One-Loop

We extend our recent study on the duality between stringy higher spin theories and free CFTs in the $SU(N)$ adjoint representation to other matrix models namely the free $SO(N)$ and $Sp(N)$ adjoint models as well as the free $U(N)\times U(M)$ bi-fundamental and $O(N)\times O(M)$ bi-vector models. After determining the spectrum of the theories in the planar limit by Polya counting, we compute the one loop vacuum energy and Casimir energy for their respective bulk duals by means of the CIRZ method that we have introduced recently. We also elaborate on possible ambiguities in the application of this method.

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arXiv2017

One-Loop Free Energy of Tensionless Type IIB String in AdS$_5\times$S$^5$

Considering the zero 't Hooft coupling limit of ${\cal N}=4$ super-Yang-Mills theory, the exact spectrum of all single-trace operators can be accessed in terms of the underlying $so(2,4)$ character. This makes it possible in turn to compute the one-loop free energy of the tensionless type IIB string theory in AdS$_5\times$S$^5$ background, with help of the recently developed method of character integral representation of zeta function (CIRZ). We calculate first the one-loop free energy of the string states in the $(p-1)$-th Regge trajectory and find the result to be $p$ times the free energy of a single ${\cal N}=4$ Maxwell multiplet. The full one-loop free energy is hence proportional to the divergent series $\sum_{p=2}^\infty p\,$. The divergence arises as a result of interrupting the regularization procedure in an intermediate stage. With a reorganization of states, we extract the finite part of free energy after summing over the Regge trajectories. This way gives us a finite result which is minus of the free energy of the ${\cal N}=4$ multiplet. Hence, this bulk one-loop result matches the -1 term in the $N^2-1$ factor of the boundary result.

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arXiv2016

A Note on Vectorial AdS$_5$/CFT$_4$ Duality for Spin-$j$ Boundary Theory

The vectorial holographic correspondences between higher-spin theories in AdS$_5$ and free vector models on the boundary are extended to the cases where the latter is described by free massless spin-$j$ field. The dual higher-spin theory in the bulk does not include gravity and can only be defined on rigid AdS$_5$ background with $S^4$ boundary. We discuss various properties of these rather special higher-spin theories and calculate their one-loop free energies. We show that the result is proportional to the same quantity for spin-$j$ doubleton treated as if it is a AdS$_5$ field. Finally, we consider even more special case where the boundary theory itself is given by an infinite tower of massless higher-spin fields.

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arXiv2016

Weyl Action of Two-Column Mixed-Symmetry Field and Its Factorization Around (A)dS Space

We investigate the four-derivative free Weyl action for two-column mixed-symmetry field that makes use of maximal gauge symmetries. In flat space, the action can be uniquely determined from gauge and Weyl (trace shift) symmetry requirements. We show that there is a smooth and unique deformation of the flat action to (A)dS which keeps the same amount of gauge symmetries. This action admits a factorization into two distinct two-derivative actions having gauge parameters of different Young diagrams. Hence, this factorization pattern naturally extends that of the Weyl actions of symmetric higher spin fields to mixed-symmetry cases. The mass-deformation for these actions can be realized preserving one of the gauge symmetries. Although generically non-unitary, in special dimensions, unitarity is achieved selecting different mass deformations for dS and AdS. We consider particular examples of our construction such as New Massive Gravity in three dimensions, linearized bigravity in four dimensions and their arbitrary dimensional generalizations.

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arXiv2016

On the Holography of Free Yang-Mills

We study the AdS$_5$/CFT$_4$ duality where the boundary CFT is free Yang-Mills theory with gauge group SU(N). At the planar level we use the spectrum and correlation functions of the boundary theory to explicate features of the bulk theory. Further, by computing the one-loop partition function of the bulk theory using the methods of arXiv:1603.05387, we argue that the bulk coupling constant should be shifted to $N^2$ from $N^2-1$. Similar conclusions are reached by studying the dualities in thermal AdS$_5$ with $S^1\times S^3$ boundary.

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arXiv2016

Spinor-Helicity Three-Point Amplitudes from Local Cubic Interactions

We make an explicit link between the cubic interactions of off-shell fields and the on-shell three-point amplitudes in four dimensions. Both the cubic interactions and the on-shell three-point amplitudes had been independently classified in the literature, but their relation has not been made explicit. The aim of this note is to provide such a relation and discuss similarities and differences of their constructions. For the completeness of our analysis, we also derive the covariant form of all parity-odd massless vertices.

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arXiv2016

One-loop Test of Free SU(N) Adjoint Model Holography

We consider the holographic duality where the CFT side is given by $SU(N)$ adjoint free scalar field theory. Compared to the vector models, the set of single trace operators is immensely extended so that the corresponding AdS theory also contains infinitely many massive higher spin fields on top of the massless ones. We compute the one-loop vacuum energy of these AdS fields to test this duality at the subleading order in large $N$ expansion. The determination of the bulk vacuum energy requires a proper scheme to sum up the infinitely many contributions. For that, we develop a new method and apply it first to calculate the vacuum energies for the first few `Regge trajectories' in AdS$_4$ and AdS$_5$. In considering the full vacuum energy of AdS theory dual to a matrix model CFT, we find that there exist more than one available prescriptions for the one-loop vacuum energy. Taking a particular prescription, we determine the full vacuum energy of the AdS$_5$ theory, whereas the AdS$_4$ calculation still remains technically prohibitive. This result shows that the full vacuum energy of the AdS$_5$ theory coincides with minus of the free energy of a single scalar field on the boundary. This is analogous to the $O(N)$ vector model case, hence suggests an interpretation of the \emph{positive} shift of the bulk coupling constant, i.e. from $N^2-1$ to $N^2$.

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arXiv2016

Rainbow Vacua of Colored Higher Spin Gravity in Three Dimensions

We study the color-decoration of higher-spin (anti)-de Sitter gravity in three dimensions. We show that the rainbow vacua, which we found recently for the colored gravity theory, also pertain in the colored higher-spin theory. The color singlet spin-two plays the role of first fundamental form (metric). The difference is that when spontaneous breaking of color symmetry takes place, the Goldstone modes of massless spin-two combine with all other spins and become the maximal-depth partially massless fields of the highest spin in the theory, forming a Regge trajectory.

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arXiv2016

Rainbow Valley of Colored (Anti) de Sitter Gravity in Three Dimensions

We propose a theory of three-dimensional (anti) de Sitter gravity carrying Chan-Paton color charges. We define the theory by Chern-Simons formulation with the gauge algebra $(\mathfrak{gl}_{2}\oplus \mathfrak{gl}_{2})\otimes \mathfrak{u}(N)$, obtaining a color-decorated version of interacting spin-one and spin-two fields. We also describe the theory in metric formulation and show that, among $N^{2}$ massless spin-two fields, only the singlet one plays the role of metric graviton whereas the rest behave as \emph{colored spinning matter} that strongly interacts at large $N$. Remarkably, these \emph{colored spinning matter} acts as Higgs field and generates a non-trivial potential of staircase shape. At each extremum labelled by $k = 0, \ldots, [\frac{N-1}2]$, the $\mathfrak{u}(N)$ color gauge symmetry is spontaneously broken down to $\mathfrak{u}(N-k)\oplus \mathfrak{u}(k)$ and provides different (A)dS backgrounds with the cosmological constants $\big(\frac{N}{N-2k}\big)^{2}\,Ł$\,. When this symmetry breaking takes place, the spin-two Goldstone modes combine with (or are eaten by) the spin-one gauge fields to become partially-massless spin-two fields. We discuss various aspects of this theory and highlight physical implications.

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arXiv2015

Partially-massless higher-spin algebras and their finite-dimensional truncations

The global symmetry algebras of partially-massless (PM) higher-spin (HS) fields in (A)dS$_{d+1}$ are studied. The algebras involving PM generators up to depth $2\,(\ell-1)$ are defined as the maximal symmetries of free conformal scalar field with $2\,\ell$ order wave equation in $d$ dimensions. We review the construction of these algebras by quotienting certain ideals in the universal enveloping algebra of $(A)dS_{d+1}$ isometries. We discuss another description in terms of Howe duality and derive the formula for computing trace in these algebras. This enables us to explicitly calculate the bilinear form for this one-parameter family of algebras. In particular, the bilinear form shows the appearance of additional ideal for any non-negative integer values of $\ell-d/2\,$, which coincides with the annihilator of the one-row $\ell$-box Young diagram representation of $\mathfrak{so}_{d+2}\,$. Hence, the corresponding finite-dimensional coset algebra spanned by massless and PM generators is equivalent to the symmetries of this representation.

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arXiv2015

Notes on higher-spin algebras: minimal representations and structure constants

The higher-spin (HS) algebras so far known can be interpreted as the symmetries of the minimal representation of the isometry algebra. After discussing this connection briefly, we generalize this concept to any classical Lie algebras and consider the corresponding HS algebras. For sp(2N) and so(N), the minimal representations are unique so we get unique HS algebras. For sl(N), the minimal representation has one-parameter family, so does the corresponding HS algebra. The so(N) HS algebra is what underlies the Vasiliev theory while the sl(2) one coincides with the 3D HS algebra hs[lambda]. Finally, we derive the explicit expression of the structure constant of these algebras --- more precisely, their bilinear and trilinear forms. Several consistency checks are carried out for our results.

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arXiv2014

No-Go Theorems for Unitary and Interacting Partially Massless Spin-Two Fields

We examine the generic theory of a partially massless (PM) spin-two field interacting with gravity in four dimensions from a bottom-up perspective. By analyzing the most general form of the Lagrangian, we first show that if such a theory exists, its de Sitter background must admit either so(1, 5) or so(2, 4) global symmetry depending on the relative sign of the kinetic terms: the former for a positive sign the latter for a negative sign. Further analysis reveals that the coupling constant of the PM cubic self-interaction must be fixed with a purely imaginary number in the case of a positive sign. We conclude that there cannot exist a unitary theory of a PM spin-two field coupled to Einstein gravity with a perturbatively local Lagrangian. In the case of a negative sign we recover conformal gravity. As a special case of our analysis, it is shown that the PM limit of massive gravity also lacks the PM gauge symmetry.

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arXiv2014

Cubic-interaction-induced deformations of higher-spin symmetries

The deformations of higher-spin symmetries induced by cubic interactions of symmetric massless bosonic fields are analyzed within the metric-like formalism. Our analysis amends the existing classification according to gauge-algebra deformations taking into account also gauge-transformation deformations. In particular, we identify a class of couplings which leave the gauge algebra Abelian but deform one (out of three) gauge transformation, and another class of couplings which deform all three gauge transformations in (A)dS but only two in the flat-space limit. The former class is related to higher-spin algebra multiplets (representations of the global algebra) together with the massless-massive-massive couplings, which we also briefly discuss. The latter class is what makes (A)dS a distinguished background for higher-spin interactions and includes in particular the gravitational interactions of higher-spin fields, retrospectively accounting for the Fradkin-Vasiliev solution to the Aragon-Deser problem. We also study the restriction of gauge symmetries to global symmetries (higher-spin algebra) discussing the invariant bilinear form and the cyclicity of the structure constants. A possible generalization of the analysis to partially-massless fields is also commented.

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