18 research outputs found
Basso-Dixon Correlators in Two-Dimensional Fishnet CFT
We compute explicitly the two-dimensional version of Basso-Dixon type
integrals for the planar four-point correlation functions given by conformal
fishnet Feynman graphs. These diagrams are represented by a fragment of a
regular square lattice of power-like propagators, arising in the recently
proposed integrable bi-scalar fishnet CFT. The formula is derived from first
principles, using the formalism of separated variables in integrable SL(2,C)
spin chain. It is generalized to anisotropic fishnet, with different powers for
propagators in two directions of the lattice.Comment: 30 pages, 13 figures, v2: improved formulas, typos correcte
Hexagonalization of Fishnet integrals II: overlaps and multi-point correlators
This work presents the building-blocks of an integrability-based
representation for multi-point Fishnet Feynman integrals with any number of
loops. Such representation relies on the quantum separation of variables (SoV)
of a non-compact spin-chain with symmetry explained in the first
paper of this series. The building-blocks of the SoV representation are
overlaps of the wave-functions of the spin-chain excitations inserted along the
edges of a triangular tile of Fishnet lattice. The zoology of overlaps is
analyzed along with various worked out instances in order to achieve compact
formulae for the generic triangular tile. The procedure of assembling the tiles
into a Fishnet integral is presented exhaustively. The present analysis
describes multi-point correlators with disk topology in the bi-scalar limit of
planar -deformed SYM theory, and it verifies some
conjectural formulae for hexagonalization of Fishnets CFTs present in the
literature. The findings of this work are suitable of generalization to a wider
class of Feynman diagrams.Comment: 31 pages (body), 13 pages (appendices); 49 figures; v2: typos
corrected, reference adde
Bi-scalar integrable CFT at any dimension
We propose a -dimensional generalization of bi-scalar conformal
quantum field theory recently introduced by G\"{u}rdogan and one of the authors
as a strong-twist double scaling limit of -deformed SYM
theory. Similarly to the case, this D-dimensional CFT is also dominated by
"fishnet" Feynman graphs and is integrable in the planar limit. The dynamics of
these graphs is described by the integrable conformal spin chain.
In it is the analogue of L. Lipatov's spin chain for
the Regge limit of , but with the spins instead of .
Generalizing recent results of Grabner, Gromov, Korchemsky and one of the
authors to any we compute exactly, at any coupling, a four point
correlation function, dominated by the simplest fishnet graphs of cylindric
topology, and extract from it exact dimensions of R-charge 2 operators with any
spin and some of their OPE structure constants.Comment: 5 pages, 4 figures, v2: typos corrected, v3: as accepted for
publication on Physical Review Letter
Stampedes I: Fishnet OPE and Octagon Bootstrap with Nonzero Bridges
Some quantities in quantum field theory are dominated by so-called
and can be re-summed to all loop orders. In this work
we introduce a notion of which is a simple time-evolution
of a bunch of particles which start their life in a corner - on the very right
say - and their way to the opposite corner - on the left -
through the repeated action of a quantum Hamiltonian. Such stampedes govern
leading logs quantities in certain quantum field theories. The leading
euclidean OPE limit of correlation functions in the fishnet theory and null
double-scaling limits of correlators in SYM are notable
examples. As an application, we use these results to extend the beautiful
bootstrap program of Coronado [1] to all octagons functions with arbitrary
diagonal bridge length.Comment: 33 pages, 18 figure
Multipoint fishnet Feynman diagrams: sequential splitting
We study fishnet Feynman diagrams defined by a certain triangulation of a
planar n-gon, with massless scalars propagating along and across the cuts. Our
solution theory uses the technique of Separation of Variables, in combination
with the theory of symmetric polynomials and Mellin space. The n-point
split-ladders are solved by a recursion where all building blocks are made
fully explicit. In particular, we find an elegant formula for the coefficient
functions of the light-cone leading logs. When the diagram grows into a
fishnet, we obtain new results exploiting a Cauchy identity decomposition of
the measure over separated variables. This leads to an elementary proof of the
Basso-Dixon formula at 4-points, while at n-points it provides a natural
OPE-like stratification of the diagram. Finally, we propose an independent
approach based on ``stampede" combinatorics to study the light-cone behaviour
of the diagrams as the partition function of a certain vertex model.Comment: Letter: 5 pages, 5 figures; Supplemental material: 21 pages, 8
figure
The Loom for General Fishnet CFTs
We propose a broad class of -dimensional conformal field theories of
adjoint scalar fields generalising the 4 Fishnet CFT (FCFT)
discovered by \"O. G\"urdogan and one of the authors as a special limit of
-deformed SYM theory. In the planar limit
the FCFTs are dominated by the ``fishnet" planar Feynman graphs. These graphs
are explicitly integrable, as was shown long ago by A. Zamolodchikov. The
Zamolodchikov's construction, based on the dual Baxter lattice (straight lines
on the plane intersecting at arbitrary slopes) and the star-triangle
identities, can serve as a ``loom" for ``weaving" the Feynman graphs of these
FCFTs, with certain types of propagators, at any . The Baxter lattice with
different slopes and any number of lines parallel to those, generates an
FCFT consisting of fields and a certain number of chiral vertices of
different valences with distinguished couplings. These non-unitary, logarithmic
CFTs enjoy certain reality properties for their spectrum due to a symmetry
similar to the PT-invariance of non-hermitian hamiltonians proposed by C.
Bender. We discuss in more detail the theories generated by a loom with
, and the generalisation of the loom FCFTs for spinning fields in
4.Comment: 35 pages, 21 figure
Stampedes II: Null Polygons in Conformal Gauge Theory
We consider correlation functions of single trace operators approaching the
cusps of null polygons in a double-scaling limit where so-called are held fixed and the
t'Hooft coupling is small. With the help of stampedes, symbols and educated
guesses, we find that any such correlator can be uniquely fixed through a set
of coupled lattice PDEs of Toda type with several intriguing novel features.
These results hold for most conformal gauge theories with a large number of
colours, including planar SYM.Comment: 8 pages, 7 figure
Quantum Trace Formulae for the Integrals of the Hyperbolic Ruijsenaars-Schneider model
We conjecture the quantum analogue of the classical trace formulae for the
integrals of motion of the quantum hyperbolic Ruijsenaars-Schneider model. This
is done by departing from the classical construction where the corresponding
model is obtained from the Heisenberg double by the Poisson reduction
procedure. We also discuss some algebraic structures associated to the Lax
matrix in the classical and quantum theory which arise upon introduction of the
spectral parameter.Comment: 35 pages, v2 as accepted by JHE