1,352 research outputs found

### Relating prepotentials and quantum vacua of N=1 gauge theories with different tree-level superpotentials

We consider N=1 supersymmetric U(N) gauge theories with Z_k symmetric
tree-level superpotentials W for an adjoint chiral multiplet. We show that (for
integer 2N/k) this Z_k symmetry survives in the quantum effective theory as a
corresponding symmetry of the effective superpotential W_eff(S_i) under
permutations of the S_i. For W(x)=^W(h(x)) with h(x)=x^k, this allows us to
express the prepotential F_0 and effective superpotential W_eff on certain
submanifolds of the moduli space in terms of an ^F_0 and ^W_eff of a different
theory with tree-level superpotential ^W. In particular, if the Z_k symmetric
polynomial W(x) is of degree 2k, then ^W is gaussian and we obtain very
explicit formulae for F_0 and W_eff. Moreover, in this case, every vacuum of
the effective Veneziano-Yankielowicz superpotential ^W_eff is shown to give
rise to a vacuum of W_eff. Somewhat surprisingly, at the level of the
prepotential F_0(S_i) the permutation symmetry only holds for k=2, while it is
anomalous for k>2 due to subtleties related to the non-compact period
integrals. Some of these results are also extended to general polynomial
relations h(x) between the tree-level superpotentials.Comment: 27 pages, 10 figures, modified version to appear in JHEP, discussion
of the physical meaning of the Z_k symmetry adde

### Higher Spins & Strings

It is natural to believe that the free symmetric product orbifold CFT is dual
to the tensionless limit of string theory on AdS3 x S3 x T4. At this point in
moduli space, string theory is expected to contain a Vasiliev higher spin
theory as a subsector. We confirm this picture explicitly by showing that the
large level limit of the N=4 cosets of arXiv:1305.4181, that are dual to a
higher spin theory on AdS3, indeed describe a closed subsector of the symmetric
product orbifold. Furthermore, we reorganise the full partition function of the
symmetric product orbifold in terms of representations of the higher spin
algebra (or rather its $W_{\infty}$ extension). In particular, the unbroken
stringy symmetries of the tensionless limit are captured by a large chiral
algebra which we can describe explicitly in terms of an infinite sum of
$W_{\infty}$ representations, thereby exhibiting a vast extension of the
conventional higher spin symmetry.Comment: 47 pages; ancillary file included; v2. typos corrected, minor changes
in Sec.

### Tensionless String Spectra on ${\rm AdS}_3$

The spectrum of superstrings on ${\rm AdS}_3 \times {\rm S}^3 \times
\mathbb{M}_4$ with pure NS-NS flux is analysed for the background where the
radius of the AdS space takes the minimal value $(k=1)$. Both for
$\mathbb{M}_4={\rm S}^3 \times {\rm S}^1$ and $\mathbb{M}_4 = \mathbb{T}^4$ we
show that there is a special set of physical states, coming from the bottom of
the spectrally flowed continuous representations, which agree in precise detail
with the single particle spectrum of a free symmetric product orbifold. For the
case of ${\rm AdS}_3 \times {\rm S}^3 \times \mathbb{T}^4$ this relies on
making sense of the world-sheet theory at $k=1$, for which we make a concrete
proposal. We also comment on the implications of this striking result.Comment: 20 pages, LaTe

### Worldsheet Properties of Extremal Correlators in AdS/CFT

We continue to investigate planar four point worldsheet correlators of string
theories which are conjectured to be duals of free gauge theories. We focus on
the extremal correlators <Tr(Z^{J_1}(x)) Tr(Z^{J_2}(y)) Tr(Z^{J_3}(z))
Tr(\bar{Z}^{J}(0))> of $N = 4$ SYM theory, and construct the corresponding
worldsheet correlators in the limit when the $J_i >> 1$. The worldsheet
correlator gets contributions, in this limit, from a whole family of Feynman
graphs. We find that it is supported on a {\it curve} in the moduli space
parametrised by the worldsheet crossratio. In a further limit of the spacetime
correlators we find this curve to be the unit circle. In this case, we also
check that the entire worldsheet correlator displays the appropriate crossing
symmetry. The non-renormalization of the extremal correlators in the 't Hooft
coupling offers a potential window for a comparison of these results with those
from strong coupling.Comment: 27 pages, 5 figure

### Stringy AdS3 from the Worldsheet

We investigate the behaviour of the bosonic string on AdS3 with H-flux at
stringy scales, looking in particular for a `tensionless' limit in which there
are massless higher spin gauge fields. We do this by revisiting the physical
spectrum of the sl(2,R)$_k$ WZW model and considering the limit in which k
becomes small. At k=3 we find that there is an infinite stringy tower of
massless higher spin fields which are part of a continuum of light states. This
can be viewed as a novel tensionless limit, which appears to be distinct from
that inferred from the symmetric orbifold description of superstring AdS3
vacua.Comment: 13 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

### Bubbling Supertubes and Foaming Black Holes

We construct smooth BPS three-charge geometries that resolve the zero-entropy
singularity of the U(1) x U(1) invariant black ring. This singularity is
resolved by a geometric transition that results in geometries without any
branes sources or singularities but with non-trivial topology. These geometries
are both ground states of the black ring, and non-trivial microstates of the
D1-D5-P system. We also find the form of the geometries that result from the
geometric transition of N zero-entropy black rings, and argue that, in general,
such geometries give a very large number of smooth bound-state three-charge
solutions, parameterized by 6N functions. The generic microstate solution is
specified by a four-dimensional hyper-Kahler geometry of a certain signature,
and contains a ``foam'' of non-trivial two-spheres. We conjecture that these
geometries will account for a significant part of the entropy of the D1-D5-P
black hole, and that Mathur's conjecture might reduce to counting certain
hyper-Kahler manifolds.Comment: 40 pages, harvmac. v2 references added, typo correcte

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