1,842 research outputs found
The Large N 't Hooft Limit of Kazama-Suzuki Model
We consider N=2 Kazama-Suzuki model on CP^N=SU(N+1)/SU(N)xU(1). It is known
that the N=2 current algebra for the supersymmetric WZW model, at level k, is a
nonlinear algebra. The N=2 W_3 algebra corresponding to N=2 was recovered from
the generalized GKO coset construction previously. For N=4, we construct one of
the higher spin currents, in N=2 W_5 algebra, with spins (2, 5/2, 5/2, 3). The
self-coupling constant in the operator product expansion of this current and
itself depends on N as well as k explicitly. We also observe a new higher spin
primary current of spins (3, 7/2, 7/2, 4). From the behaviors of N=2, 4 cases,
we expect the operator product expansion of the lowest higher spin current and
itself in N=2 W_{N+1} algebra. By taking the large (N, k) limit on the various
operator product expansions in components, we reproduce, at the linear order,
the corresponding operator product expansions in N=2 classical
W_{\infty}^{cl}[\lambda] algebra which is the asymptotic symmetry of the higher
spin AdS_3 supergravity found recently.Comment: 44 pages; the two typos in the first paragraph of page 23 corrected
and to appear in JHE
The Operator Product Expansion of the Lowest Higher Spin Current at Finite N
For the N=2 Kazama-Suzuki(KS) model on CP^3, the lowest higher spin current
with spins (2, 5/2, 5/2,3) is obtained from the generalized GKO coset
construction. By computing the operator product expansion of this current and
itself, the next higher spin current with spins (3, 7/2, 7/2, 4) is also
derived. This is a realization of the N=2 W_{N+1} algebra with N=3 in the
supersymmetric WZW model. By incorporating the self-coupling constant of lowest
higher spin current which is known for the general (N,k), we present the
complete nonlinear operator product expansion of the lowest higher spin current
with spins (2, 5/2, 5/2, 3) in the N=2 KS model on CP^N space. This should
coincide with the asymptotic symmetry of the higher spin AdS_3 supergravity at
the quantum level. The large (N,k) 't Hooft limit and the corresponding
classical nonlinear algebra are also discussed.Comment: 62 pages; the footnotes added, some redundant appendices removed, the
presentations in the whole paper improved and to appear in JHE
The Primary Spin-4 Casimir Operators in the Holographic SO(N) Coset Minimal Models
Starting from SO(N) current algebra, we construct two lowest primary higher
spin-4 Casimir operators which are quartic in spin-1 fields. For N is odd, one
of them corresponds to the current in the WB_{\frac{N-1}{2}} minimal model. For
N is even, the other corresponds to the current in the WD_{\frac{N}{2}} minimal
model. These primary higher spin currents, the generators of wedge subalgebra,
are obtained from the operator product expansion of fermionic (or bosonic)
primary spin-N/2 field with itself in each minimal model respectively. We
obtain, indirectly, the three-point functions with two real scalars, in the
large N 't Hooft limit, for all values of the 't Hooft coupling which should be
dual to the three-point functions in the higher spin AdS_3 gravity with matter.Comment: 65 pages; present the main results only and to appear in JHEP where
one can see the Appendi
On the coset duals of extended higher spin theories
We study the holographic duality between the M x M matrix extension of
Vasiliev higher spin theories on AdS3 and the large N limit of SU(N+M)/SU(N) x
U(1) type cosets. We present a simplified proof for the agreement of the
spectra and clarify the relation between this duality and the version in which
the cosets are replaced by Kazama-Suzuki models of Grassmannian type.Comment: 27 pages, 1 tabl
Higher spin AdS_3 holography with extended supersymmetry
We propose a holographic duality between a higher spin AdS_3 gravity with
so(p) extended supersymmetry and a large N limit of a 2-dimensional
Grassmannian-like model with a specific critical level k=N and a non-diagonal
modular invariant. As evidence, we show the match of one-loop partition
functions. Moreover, we construct symmetry generators of the coset model for
low spins which are dual to gauge fields in the supergravity. Further, we
discuss a possible relation to superstring theory by noticing an N=3
supersymmetry of critical level model at finite k,N. In particular, we examine
BPS states and marginal deformations. Inspired by the supergravity side, we
also propose and test another large N CFT dual obtained as a Z_2 automorphism
truncation of a similar coset model, but at a non-critical level.Comment: 44 pages, published versio
The Coset Spin-4 Casimir Operator and Its Three-Point Functions with Scalars
We find the GKO coset construction of the dimension 4 Casimir operator that
contains the quartic WZW currents contracted with completely symmetric SU(N)
invariant tensors of ranks 4, 3, and 2. The requirements, that the operator
product expansion with the diagonal current is regular and it should be primary
under the coset Virasoro generator of dimension 2, fix all the coefficients in
spin-4 current, up to two unknown coefficients. The operator product expansion
of coset primary spin-3 field with itself fixes them completely. We compute the
three-point functions with scalars for all values of the 't Hooft coupling in
the large N limit. At fixed 't Hooft coupling, these three-point functions are
dual to that found by Chang and Yin recently in the undeformed AdS_3 bulk
theory (higher spin gravity with matter).Comment: 65 pages; the ambiguity for the two coefficient functions is
clarified and the abstract, the introduction, the subsection 3.4 and the
conclusion are improved and to appear in JHE
Triality in Minimal Model Holography
The non-linear W_{\infty}[\mu] symmetry algebra underlies the duality between
the W_N minimal model CFTs and the hs[\mu] higher spin theory on AdS_3. It is
shown how the structure of this symmetry algebra at the quantum level, i.e. for
finite central charge, can be determined completely. The resulting algebra
exhibits an exact equivalence (a`triality') between three (generically)
distinct values of the parameter \mu. This explains, among other things, the
agreement of symmetries between the W_N minimal models and the bulk higher spin
theory. We also study the consequences of this triality for some of the
simplest W_{\infty}[\mu] representations, thereby clarifying the analytic
continuation between the`light states' of the minimal models and conical defect
solutions in the bulk. These considerations also lead us to propose that one of
the two scalar fields in the bulk actually has a non-perturbative origin.Comment: 29 pages; v2. Typos correcte
Limits of minimal models and continuous orbifolds
The lambda=0 't Hooft limit of the 2d W_N minimal models is shown to be
equivalent to the singlet sector of a free boson theory, thus paralleling
exactly the structure of the free theory in the Klebanov-Polyakov proposal. In
2d, the singlet sector does not describe a consistent theory by itself since
the corresponding partition function is not modular invariant. However, it can
be interpreted as the untwisted sector of a continuous orbifold, and this point
of view suggests that it can be made consistent by adding in the appropriate
twisted sectors. We show that these twisted sectors account for the `light
states' that were not included in the original 't Hooft limit. We also show
that, for the Virasoro minimal models (N=2), the twisted sector of our orbifold
agrees precisely with the limit theory of Runkel & Watts. In particular, this
implies that our construction satisfies crossing symmetry.Comment: 33 pages; v2: minor improvements and references added, published
versio
N=1 extension of minimal model holography
The CFT dual of the higher spin theory with minimal N = 1 spectrum is
determined. Unlike previous examples of minimal model holography, there is no
free parameter beyond the central charge, and the CFT can be described in terms
of a non-diagonal modular invariant of the bosonic theory at the special value
of the 't Hooft parameter lambda=1/2. As evidence in favour of the duality we
show that the symmetry algebras as well as the partition functions agree
between the two descriptions.Comment: 28 page
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