43 research outputs found
Three-Point Functions in N=2 Higher-Spin Holography
The CP^N Kazama-Suzuki models with the non-linear chiral algebra
SW_infinity[lambda] have been conjectured to be dual to the fully
supersymmetric Prokushkin-Vasiliev theory of higher-spin gauge fields coupled
to two massive N=2 multiplets on AdS_3. We perform a non-trivial check of this
duality by computing three-point functions containing one higher-spin gauge
field for arbitrary spin s and deformation parameter lambda from the bulk
theory, and from the boundary using a free ghost system based on the linear
sw_infinity[lambda] algebra. We find an exact match between the two
computations. In the 't Hooft limit, the three-point functions only depend on
the wedge subalgebra shs[lambda] and the results are equivalent for any theory
with such a subalgebra. In the process we also find the emergence of N=2
superconformal symmetry near the AdS_3 boundary by computing holographic OPE's,
consistently with a recent analysis of asymptotic symmetries of higher-spin
supergravity.Comment: 40 pages; This work is based on the first author's MSc thesis,
submitted to the Niels Bohr Institute, University of Copenhagen, in November
2012. v2: References added. v3: Minor typos fixe
Flux Superpotential in Heterotic M-theory
We derive the most general flux-induced superpotential for N=1 M-theory
compactifications on seven-dimensional manifolds with SU(3) structure. Imposing
the appropriate boundary conditions, this result applies for heterotic
M-theory. It is crucial for the latter to consider SU(3) and not G_2 group
structure on the seven-dimensional internal space. For a particular background
that differs from CY(3) x S^1/Z_2 only by warp factors, we investigate the
flux-generated scalar potential as a function of the orbifold length. We find a
positive cosmological constant minimum, however at an undesirably large value
of this length. Hence the flux superpotential alone is not enough to stabilize
the orbifold length at a de Sitter vacuum. But it does modify substantially the
interplay between the previously studied non-perturbative effects, possibly
reducing the significance of open membrane instantons while underlining the
importance of gaugino condensation.Comment: 33 pages; minor clarifications, reference adde
Non-integrability and Chaos with Unquenched Flavor
We study (non-)integrability and the presence of chaos in gravity dual
backgrounds of strongly coupled gauge theories with unquenched flavor,
specifically of the four-dimensional N=2 super Yang-Mills theory and the
three-dimensional ABJM theory. By examining string motion on the geometries
corresponding to backreacted D3/D7 and D2/D6 systems, we show that integrable
theories with quenched flavor become non-integrable when the virtual quark
loops are taken into account. For the string solutions in the backreacted D3/D7
system, we compute the leading Lyapunov exponent which turns out to saturate to
a positive value as the number of flavors increases. The exponent depends very
weakly on the number of flavors when they approach the number of colors. This
suggests that once a particular flavor number in the theory is reached, a
further increase does not lead to more severe chaotic phenomena, implying
certain saturation effects on chaos.Comment: 34 pages, 6 figures; v2: minor additions, references adde
On the combinatorics of partition functions in AdS3/LCFT2
Three-dimensional Topologically Massive Gravity at its critical point has
been conjectured to be holographically dual to a Logarithmic CFT. However, many
details of this correspondence are still lacking. In this work, we study the
1-loop partition function of Critical Cosmological Topologically Massive
Gravity, previously derived by Gaberdiel, Grumiller and Vassilevich, and show
that it can be usefully rewritten as a Bell polynomial expansion. We also show
that there is a relationship between this Bell polynomial expansion and the
Plethystic Exponential. Our reformulation allows us to match the TMG partition
function to states on the CFT side, including the multi-particle states of t
(the logarithmic partner of the CFT stress tensor) which had previously been
elusive. We also discuss the appearance of a ladder action between the
different multi-particle sectors in the partition function, which induces an
interesting sl(2) structure on the n-particle components of the partition
function.Comment: 26 pages. Typos fixed, references and clarifications adde
On Marginal Deformations and Non-Integrability
We study the interplay between a particular marginal deformation of super Yang-Mills theory, the deformation, and integrability in
the holographic setting. Using modern methods of analytic non-integrability of
Hamiltonian systems, we find that, when the parameter takes imaginary
values, classical string trajectories on the dual background become
non-integrable. We expect the same to be true for generic complex
parameter. By exhibiting the Poincar\'e sections and phase space trajectories
for the generic complex case, we provide numerical evidence of strong
sensitivity to initial conditions. Our findings agree with expectations from
weak coupling that the complex deformation is non-integrable and
provide a rigorous argument beyond the trial and error approach to
non-integrability.Comment: 19 pages, 9 figure
Marginal deformations and quasi-Hopf algebras
We establish the existence of a quasi-Hopf algebraic structure underlying the
Leigh-Strassler N=1 superconformal marginal deformations of the N=4
Super-Yang-Mills theory. The scalar-sector R-matrix of these theories, which is
related to their one-loop spin chain Hamiltonian, does not generically satisfy
the Quantum Yang-Baxter Equation. By constructing a Drinfeld twist which
relates this R-matrix to that of the N=4 SYM theory, but also produces a
non-trivial co-associator, we show that the generic Leigh-Strassler R-matrix
satisfies the quasi-Hopf version of the QYBE. We also use the twist to define a
suitable star product which directly relates the N=4 SYM superpotential to that
of the marginally deformed gauge theories. We expect our results to be relevant
to studies of integrability (and its breaking) in these theories, as well as to
provide useful input for supergravity solution-generating techniques.Comment: 38 pages, 2 figures, Mathematica notebook submitted. v2: Typos fixed,
references adde
Dynamical Spin Chains in 4D SCFTs
This is the first in a series of papers devoted to the study of spin chains
capturing the spectral problem of 4d SCFTs in the planar limit.
At one loop and in the quantum plane limit, we discover a quasi-Hopf symmetry
algebra, defined by the -matrix read off from the superpotential. This
implies that when orbifolding the symmetry algebra down to the
one and then marginaly deforming, the broken generators are not
lost, but get upgraded to quantum generators. Importantly, we demonstrate that
these chains are dynamical, in the sense that their Hamiltonian depends on a
parameter which is dynamically determined along the chain. At one loop we map
the holomorphic SU(3) scalar sector to a dynamical 15-vertex model, which
corresponds to an RSOS model, whose adjacency graph can be read off from the
gauge theory quiver/brane tiling. One scalar SU(2) sub-sector is described by
an alternating nearest-neighbour Hamiltonian, while another choice of SU(2)
sub-sector leads to a dynamical dilute Temperley-Lieb model. These sectors have
a common vacuum state, around which the magnon dispersion relations are
naturally uniformised by elliptic functions. Concretely, for the
quiver theory we study these dynamical chains by solving the one- and
two-magnon problems with the coordinate Bethe ansatz approach. We confirm our
analytic results by numerical comparison with the explicit diagonalisation of
the Hamiltonian for short closed chains.Comment: 88 pages, 14 Figure
Non-integrability and chaos with unquenched flavor
We study (non-)integrability and the presence of chaos in gravity dual backgrounds of
strongly coupled gauge theories with unquenched
avor, speci cally of the four-dimensional
N = 2 super Yang-Mills theory and the three-dimensional ABJM theory. By examining string
motion on the geometries corresponding to backreacted D3/D7 and D2/D6 systems, we show
that integrable theories with quenched
avor become non-integrable when the virtual quark
loops are taken into account. For the string solutions in the backreacted D3/D7 system, we
compute the leading Lyapunov exponent which turns out to saturate to a positive value as the
number of
avors increases. The exponent depends very weakly on the number of
avors when
they approach the number of colors. This suggests that once a particular
avor number in the
theory is reached, a further increase does not lead to more severe chaotic phenomena, implying
certain saturation e ects on chaos.Article funded by SCOAP.http://www.springer.com/physics/particle+and+nuclear+physics/journal/13130am2017Physic
Non-integrability and chaos with unquenched flavor
We study (non-)integrability and the presence of chaos in gravity dual backgrounds of
strongly coupled gauge theories with unquenched
avor, speci cally of the four-dimensional
N = 2 super Yang-Mills theory and the three-dimensional ABJM theory. By examining string
motion on the geometries corresponding to backreacted D3/D7 and D2/D6 systems, we show
that integrable theories with quenched
avor become non-integrable when the virtual quark
loops are taken into account. For the string solutions in the backreacted D3/D7 system, we
compute the leading Lyapunov exponent which turns out to saturate to a positive value as the
number of
avors increases. The exponent depends very weakly on the number of
avors when
they approach the number of colors. This suggests that once a particular
avor number in the
theory is reached, a further increase does not lead to more severe chaotic phenomena, implying
certain saturation e ects on chaos.Article funded by SCOAP.http://www.springer.com/physics/particle+and+nuclear+physics/journal/13130am2017Physic