50,621 research outputs found

### Stabilizing the Richardson Algorithm by Controlling Chaos

By viewing the operations of the Richardson purification algorithm as a
discrete time dynamical process, we propose a method to overcome the
instability of the algorithm by controlling chaos. We present theoretical
analysis and numerical results on the behavior and performance of the
stabilized algorithm.Comment: Send email to [email protected] or [email protected] for uuencoded
tarred gzipped postscript files for the five figure

### Conformal bootstrap to R\'enyi entropy in 2D Liouville and super-Liouville CFTs

The R\'enyi entanglement entropy (REE) of the states excited by local
operators in two-dimensional irrational conformal field theories (CFTs),
especially in Liouville field theory (LFT) and $\mathcal{N}=1$ super-Liouville
field theory (SLFT), has been investigated. In particular, the excited states
obtained by acting on the vacuum with primary operators were considered. {We
start from evaluating the second REE in a compact $c=1$ free boson field theory
at generic radius, which is an irrational CFT. Then we focus on the two special
irrational CFTs, e.g., LFT and SLFT. In these theories, the second REE of such
local excited states becomes divergent in early and late time limits. For
simplicity, we study the memory effect of REE for the two classes of the local
excited states in LFT and SLFT. In order to restore the quasiparticles picture,
we define the difference of REE between target and reference states, which
belong to the same class. The variation of the difference of REE between early
and late time limits always coincides with the log of the ratio of the fusion
matrix elements between target and reference states. Furthermore, the locally
excited states by acting generic descendent operators on the vacuum have been
also investigated. The variation of the difference of REE is the summation of
the log of the ratio of the fusion matrix elements between the target and
reference states, and an additional normalization factor. Since the identity
operator (or vacuum state) does not live in the Hilbert space of LFT and SLFT
and no discrete terms contribute to REE in the intermediate channel, the
variation of the difference of REE between target and reference states is no
longer the log of the quantum dimension which is shown in the 1+1-dimensional
rational CFTs (RCFTs).Comment: 53 pages,add a new section (Section 2.4

### T-duality to Scattering Amplitude and Wilson Loop in Non-commutative Super Yang-Mills Theory

We first perform bosonic T-duality transformation on one of the marginal TsT
(T-duality, shift, T-duality)-deformed $AdS_5\times S_5$ spacetime, which
corresponds to 4D $\mathcal{N}=4$ non-commutative super Yang-Mills theory
(NCSYM). We then construct the solution to killing spinor equations of the
resulting background, and perform the fermionic T-duality transformation. The
final dual geometry becomes the usual $AdS_5\times S_5$ but with the constant
NS-NS B-field depending on the non-commutative parameter. As applications, we
study the gluon scattering amplitude and open string (Wilson loop) solution in
the TsT-deformed $AdS_5\times S_5$ spacetime, which are dual to the null
polygon Wilson loop and the folded string solution respectively in the final
dual geometry.Comment: 24 pages, latex, references added, published versio

### A note on connected formula for form factors

In this note we study the connected prescription, originally derived from
Witten's twistor string theory, for tree-level form factors in ${\cal N}=4$
super-Yang-Mills theory. The construction is based on the recently proposed
four-dimensional scattering equations with $n$ massless on-shell states and one
off-shell state, which we expect to work for form factors of general operators.
To illustrate the universality of the prescription, we propose compact formulas
for super form factors with chiral stress-tensor multiplet operator, and
bosonic ones with scalar operators ${\rm Tr}(\phi^m)$ for arbitrary $m$.Comment: 13 page

### An Etude on Recursion Relations and Triangulations

Following~\cite{Arkani-Hamed:2017thz}, we derive a recursion relation by
applying a one-parameter deformation of kinematic variables for tree-level
scattering amplitudes in bi-adjoint $\phi^3$ theory. The recursion relies on
properties of the amplitude that can be made manifest in the underlying
kinematic associahedron, and it provides triangulations for the latter.
Furthermore, we solve the recursion relation and present all-multiplicity
results for the amplitude: by reformulating the associahedron in terms of its
vertices, it is given explicitly as a sum of "volume" of simplicies for any
triangulation, which is an analogy of BCFW representation/triangulation of
amplituhedron for ${\cal N}=4$ SYM.Comment: 26 pages, 3 figure

### A Causal Set Black Hole

We explicitly compute the causal structure of the Schwarzschild black hole
spacetime, by providing an algorithm to decide if any pair of events is
causally related. The primary motivation for this study comes from discrete
quantum gravity, in particular the causal set approach, in which the
fundamental variables can be thought of as the causal ordering of randomly
selected events in spacetime. This work opens the way to simulating
non-conformally flat spacetimes within the causal set approach, which may allow
one to study important questions such as black hole entropy and Hawking
radiation on a full four dimensional causal set black hole.Comment: 22 pages, 9 figures, LaTeX; response to referee comment

### New Relations for Gauge-Theory and Gravity Amplitudes at Loop Level

In this letter, we extend the tree-level Kawai--Lewellen--Tye (KLT) and
Bern--Carrasco--Johansson (BCJ) amplitude relations to loop integrands of gauge
theory and gravity. By rearranging the propagators of gauge and gravity loop
integrands, we propose the first manifestly gauge- and diffeomorphism invariant
formulation of their double-copy relations. The one-loop KLT formula expresses
gravity integrands in terms of more basic gauge invariant building blocks for
gauge-theory amplitudes, dubbed partial integrands. The latter obey a one-loop
analogue of the BCJ relations, and both KLT and BCJ relations are universal to
bosons and fermions in any number of spacetime dimensions and independent on
the amount of supersymmetry. Also, one-loop integrands of Einstein--Yang--Mills
(EYM) theory are related to partial integrands of pure gauge theories.Comment: 6 pages; v2: references added, minor corrections, published version
with updated reference on work in progres

- â€¦