92 research outputs found

### Supersymmetric $\mathrm{AdS}_3$ supergravity backgrounds and holography

We analyse the conditions for $\mathrm{AdS}_3 \times \mathcal{M}_7$
backgrounds with pure NS-NS flux to be supersymmetric. We find that a necessary
condition is that $\mathcal{M}_7$ is a $\mathrm{U}(1)$-fibration over a
balanced manifold. We subsequently classify all $\mathcal{N}=(2,2)$ solutions
where $\mathcal{M}_7$ satisfies the stronger condition of being a
$\mathrm{U}(1)$-fibration over a Kahler manifold. We compute the BPS spectrum
of all the backgrounds in this classification. We assign a natural dual CFT to
the backgrounds and confirm that the BPS spectra agree, thus providing evidence
in favour of the proposal.Comment: 39 pages; v2: minor corrections and references added; v3: section 2
shortened, final version as published in JHE

### String theory on $\boldsymbol{\text{AdS}_{\mathbf{3}}}$ and the symmetric orbifold of Liouville theory

For string theory on AdS$_3$ with pure NS-NS flux a complete set of DDF
operators is constructed, from which one can read off the symmetry algebra of
the spacetime CFT. Together with an analysis of the spacetime spectrum, this
allows us to show that the CFT dual of superstring theory on ${\rm AdS}_3
\times {\rm S}^3 \times \mathbb{T}^4$ for generic NS-NS flux is the symmetric
orbifold of $({\cal N}=4$ Liouville theory$)\times \mathbb{T}^4$. For the case
of minimal flux ($k=1$), the Liouville factor disappears, and we just obtain
the symmetric orbifold of $\mathbb{T}^4$, thereby giving further support to a
previous claim. We also show that a similar analysis can be done for bosonic
string theory on ${\rm AdS}_3 \times X$.Comment: 33+10 page

### Strings on $\text{AdS}_3 \times \text{S}^3 \times \text{S}^3 \times \text{S}^1$

String theory on ${\rm AdS}_3 \times {\rm S}^3 \times {\rm S}^3 \times {\rm
S}^1$ with pure NS-NS flux and minimal flux through one of the two ${\rm
S}^3$'s is studied from a world-sheet perspective. It is shown that the
spacetime spectrum, as well as the algebra of spectrum generating operators,
matches precisely that of the symmetric orbifold of ${\rm S}^3\times
\mathrm{S}^1$ in the large $N$ limit. This gives strong support for the
proposal that these two descriptions are exactly dual to one another.Comment: 25+23 page

### The Worldsheet Dual of the Symmetric Product CFT

Superstring theory on ${\rm AdS}_3\times {\rm S}^3\times \mathbb{T}^4$ with
the smallest amount of NS-NS flux (`$k=1$') is shown to be dual to the
spacetime CFT given by the large $N$ limit of the free symmetric product
orbifold $\mathrm{Sym}^N(\mathbb{T}^4)$. To define the worldsheet theory at
$k=1$, we employ the hybrid formalism in which the ${\rm AdS}_3\times {\rm
S}^3$ part is described by the $\mathfrak{psu}(1,1|2)_1$ WZW model (which is
well defined). Unlike the case for $k\geq2$, it turns out that the string
spectrum at $k=1$ does {\it not} exhibit the long string continuum, and
perfectly matches with the large $N$ limit of the symmetric product. We also
demonstrate that the fusion rules of the symmetric orbifold are reproduced from
the worldsheet perspective. Our proposal therefore affords a tractable
worldsheet description of a tensionless limit in string theory, for which the
dual CFT is also explicitly known.Comment: 29+24 page

### A holographic dual for string theory on $\mathrm{AdS}_3 \times \mathrm{S}^3 \times \mathrm{S}^3 \times \mathrm{S}^1$

The CFT dual of string theory on $\mathrm{AdS}_3 \times \mathrm{S}^3 \times
\mathrm{S}^3 \times \mathrm{S}^1$ is conjectured to be the symmetric orbifold
of the $\mathcal{S}_\kappa$ theory, provided that one of the two $Q_5^\pm$
quantum numbers is a multiple of the other. We determine the BPS spectrum of
the symmetric orbifold in detail, and show that it reproduces precisely the BPS
spectrum that was recently calculated in supergravity. We also determine the
BPS spectrum of the world-sheet theory that is formulated in terms of WZW
models, and show that, apart from some gaps (which are reminiscent of those
that appear in the corresponding $\mathbb{T}^4$ calculation), it also
reproduces this BPS spectrum. In fact, the matching seems to work as well as
for the familiar $\mathbb{T}^4$ case, and thus our results give strong support
for this proposal.Comment: 41 pages, 2 figure

### Higher spin algebras and large $\mathcal{N}=4$ holography

A new family of higher spin algebras that arises upon restricting matrix
extensions of $\mathfrak{shs}[\lambda]$ is found. We identify coset CFTs
realising these symmetry algebras, and thus propose new higher spin-CFT dual
pairs. These higher spin theories arise naturally as a subsector of string
theory on ${\rm AdS}_3\times {\rm S}^3 \times {\rm S}^3 \times {\rm S}^1$ for
specific ratios of the radii of the two spheres.Comment: 22 page

### Holographic Weyl anomaly in string theory

We compute the worldsheet sphere partition function of string theory on
global AdS$_3$ with pure NS-NS flux. Because of an unfixed M\"obius symmetry on
the worldsheet, there is a cancellation of infinities and only a part of the
answer is unambiguous. We show that it precisely reproduces the holographic
Weyl anomaly and the ambiguous terms correspond to the possible counterterms of
the boundary CFT.Comment: 9 pages + appendi

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