286 research outputs found
Symmetries of Tree-level Scattering Amplitudes in N=6 Superconformal Chern-Simons Theory
Constraints of the osp(6|4) symmetry on tree-level scattering amplitudes in
N=6 superconformal Chern-Simons theory are derived. Supplemented by Feynman
diagram calculations, solutions to these constraints, namely the four- and
six-point superamplitudes, are presented and shown to be invariant under
Yangian symmetry. This introduces integrability into the amplitude sector of
the theory.Comment: 50 pages. v2, v3: References added, minor correction
On correlation functions of BPS operators in superconformal theories
We introduce a novel harmonic superspace for
superconformal field theories that is tailor made for the study of correlation
functions of BPS operators. We calculate a host of two- and three-point
functions in full generality and put strong constraints on the form of
four-point functions of some selected BPS multiplets. For the four-point
function of -BPS operators we obtain the associated Ward
identities by imposing the absence of harmonic singularities. The latter imply
the existence of a solvable subsector in which the correlator becomes
topological. This mechanism can be explained by cohomological reduction with
respect to a special nilpotent supercharge.Comment: 41 pages, v2: typos corrected, references adde
VOAs labelled by complex reflection groups and 4d SCFTs
We define and study a class of vertex operator algebras
labelled by complex reflection groups.
They are extensions of the super Virasoro algebra obtained by
introducing additional generators, in correspondence with the invariants of the
complex reflection group . If is a
Coxeter group, the super Virasoro algebra enhances to the
(small) superconformal algebra. With the exception of
, which corresponds to just the
algebra, these are non-deformable VOAs that exist only for a
specific negative value of the central charge. We describe a free-field
realization of in terms of
rank ghost systems, generalizing a
construction of Adamovic for the algebra at . If
is a Weyl group, is
believed to coincide with the VOA that arises from the
four-dimensional super Yang-Mills theory whose gauge algebra has Weyl group
. More generally, if is a
crystallographic complex reflection group,
is conjecturally associated to an superconformal field
theory. The free-field realization allows to determine the elusive
`-filtration' of , and thus to recover
the full Macdonald index of the parent theoryComment: 70 page
Baxter Operators and Hamiltonians for "nearly all" Integrable Closed gl(n) Spin Chains
We continue our systematic construction of Baxter Q-operators for spin
chains, which is based on certain degenerate solutions of the Yang-Baxter
equation. Here we generalize our approach from the fundamental representation
of gl(n) to generic finite-dimensional representations in quantum space. The
results equally apply to non-compact representations of highest or lowest
weight type. We furthermore fill an apparent gap in the literature, and provide
the nearest-neighbor Hamiltonians of the spin chains in question for all cases
where the gl(n) representations are described by rectangular Young diagrams, as
well as for their infinite-dimensional generalizations. They take the form of
digamma functions depending on operator-valued shifted weights.Comment: 26 pages, 1 figur
Bootstrapping string dynamics in the 6d theories
We present two complementary approaches to calculating the 2-point function
of stress tensors in the presence of a 1/2 BPS surface defect of the 6d
theories. First, we use analytical bootstrap techniques
at large to obtain the first nontrivial correction to this correlator, from
which we extract the defect CFT (dCFT) data characterising the 2d dCFT of the
1/2 BPS plane. Along the way we derive a supersymmetric inversion formula,
obtain the relevant superconformal blocks and check that crossing symmetry is
satisfied. Notably our result features a holomorphic function whose appearance
is related to the chiral algebra construction of Beem, Rastelli and van Rees.
Second, we use that chiral algebra description to obtain exact results for the
BPS sector of the dCFT, valid at any and for any choice of surface
operator. These results provide a window into the dynamics of strings of the
mysterious 6d theories.Comment: 32 pages, 3 figure
A Shortcut to the Q-Operator
Baxter's Q-operator is generally believed to be the most powerful tool for
the exact diagonalization of integrable models. Curiously, it has hitherto not
yet been properly constructed in the simplest such system, the compact spin-1/2
Heisenberg-Bethe XXX spin chain. Here we attempt to fill this gap and show how
two linearly independent operatorial solutions to Baxter's TQ equation may be
constructed as commuting transfer matrices if a twist field is present. The
latter are obtained by tracing over infinitely many oscillator states living in
the auxiliary channel of an associated monodromy matrix. We furthermore compare
and differentiate our approach to earlier articles addressing the problem of
the construction of the Q-operator for the XXX chain. Finally we speculate on
the importance of Q-operators for the physical interpretation of recent
proposals for the Y-system of AdS/CFT.Comment: 41 pages, 2 figures; v2: references added; v3: version published in
J. Stat. Mec
Bootstrap equations for N = 4 SYM with defects
This paper focuses on the analysis of superconformal
theories in the presence of a defect from the point of view of the conformal
bootstrap. We will concentrate first on the case of codimension one, where the
defect is a boundary that preserves half of the supersymmetry. After studying
the constraints imposed by supersymmetry, we will obtain the Ward identities
associated to two-point functions of -BPS operators and write
their solution as a superconformal block expansion. Due to a surprising
connection between spacetime and R-symmetry conformal blocks, our results not
only apply to superconformal theories with a boundary, but
also to three more systems that have the same symmetry algebra:
superconformal theories with a line defect,
superconformal theories with no defect, and
superconformal quantum mechanics. The superconformal algebra implies that all
these systems possess a closed subsector of operators in which the bootstrap
equations become polynomial constraints on the CFT data. We derive these
truncated equations and initiate the study of their solutions.Comment: 44 pages, 2 figures, v3: typos fixed, to appear in JHE
New N=2 superconformal field theories from S-folds
We study the four-dimensional N=2 superconformal field theories that describe
D3-branes probing the recently constructed N=2 S-folds in F-theory. We
introduce a novel, infinite class of superconformal field theories related to
S-fold theories via partial Higgsing. We determine several properties of both
the S-fold models and this new class of theories, including their central
charges, Coulomb branch spectrum, and moduli spaces of vacua, by bringing to
bear an array of field-theoretical techniques, to wit, torus-compactifications
of six-dimensional N=(1,0) theories, class S technology, and the SCFT/VOA
correspondence.Comment: 49 pages; v2: minor improvements, references adde
Free Field Realizations from the Higgs Branch
We present free field realizations for the associated vertex operator
algebras of a number of four-dimensional superconformal field
theories. Our constructions utilize an exceptionally small set of chiral bosons
whose number matches the complex dimensionality of the Higgs branch of the
superconformal field theory. In the case of theories whose Higgs branches
support additional degrees of freedom (free vector multiplets or decoupled
interacting SCFTs), the corresponding "free field realizations" include
additional ingredients: symplectic fermions in the case of vector multiplets
and a co-finite VOA in the case of a residual interacting SCFT. The
resulting picture is that the associated VOA can be constructed from the Higgs
branch effective theory via free field realization. Our constructions also
provide a natural realization of the -filtration of the associated VOA.Comment: 31 pages. v2: minor typos fixed, references adde
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