137,828 research outputs found
An Application of the Feferman-Vaught Theorem to Automata and Logics for<br> Words over an Infinite Alphabet
We show that a special case of the Feferman-Vaught composition theorem gives
rise to a natural notion of automata for finite words over an infinite
alphabet, with good closure and decidability properties, as well as several
logical characterizations. We also consider a slight extension of the
Feferman-Vaught formalism which allows to express more relations between
component values (such as equality), and prove related decidability results.
From this result we get new classes of decidable logics for words over an
infinite alphabet.Comment: 24 page
Double scaling limit of N=2 chiral correlators with Maldacena-Wilson loop
We consider conformal QCD in four dimensions and the one-point
correlator of a class of chiral primaries with the circular -BPS
Maldacena-Wilson loop. We analyze a recently introduced double scaling limit
where the gauge coupling is weak while the R-charge of the chiral primary
is large. In particular, we consider the case
, where is the complex scalar in
the vector multiplet. The correlator defines a non-trivial scaling function at
fixed and large that may be studied by
localization. For any gauge group we provide the analytic expression of
the first correction and prove its universality. In
the and theories we compute the scaling functions at order
. Remarkably, in the case the scaling function
is equal to an analogous quantity describing the chiral 2-point functions
in the same large R-charge limit. We
conjecture that this scaling function is computed at all-orders by a
SYM expectation value of a matrix model object characterizing
the one-loop contribution to the 4-sphere partition function. The conjecture
provides an explicit series expansion for the scaling function and is checked
at order by showing agreement with the available data
in the sector of chiral 2-point functions.Comment: 21 page
Quantum Computation of Scattering in Scalar Quantum Field Theories
Quantum field theory provides the framework for the most fundamental physical theories to be confirmed experimentally, and has enabled predictions of unprecedented precision. However, calculations of physical observables often require great computational complexity and can generally be performed only when the interaction strength is weak. A full understanding of the foundations and rich consequences of quantum field theory remains an outstanding challenge. We develop a quantum algorithm to compute relativistic scattering amplitudes in massive phi-fourth theory in spacetime of four and fewer dimensions. The algorithm runs in a time that is polynomial in the number of particles, their energy, and the desired precision, and applies at both weak and strong coupling. Thus, it offers exponential speedup over existing classical methods at high precision or strong coupling
Nonperturbative renormalization group approach to Lifshitz critical behaviour
The behaviour of a d-dimensional vectorial N=3 model at a m-axial Lifshitz
critical point is investigated by means of a nonperturbative renormalization
group approach that is free of the huge technical difficulties that plague the
perturbative approaches and limit their computations to the lowest orders. In
particular being systematically improvable, our approach allows us to control
the convergence of successive approximations and thus to get reliable physical
quantities in d=3.Comment: 6 pages, 3 figure
On structure constants with two spinning twist-two operators
I consider three-point functions of one protected and two unprotected
twist-two operators with spin in N=4 SYM at weak coupling. At one loop I
formulate an empiric conjecture for the dependence of the corresponding
structure constants on the spins of the operators. Using such an ansatz and
some input from explicit perturbative results, I fix completely various
infinite sets of one-loop structure constants of these three-point functions.
Finally, I determine the two-loop corrections to the structure constants for a
few fixed values of the spins of the operators.Comment: 21 page
On the fate of singularities and horizons in higher derivative gravity
We study static spherically symmetric solutions of high derivative gravity
theories, with 4, 6, 8 and even 10 derivatives. Except for isolated points in
the space of theories with more than 4 derivatives, only solutions that are
nonsingular near the origin are found. But these solutions cannot smooth out
the Schwarzschild singularity without the appearance of a second horizon. This
conundrum, and the possibility of singularities at finite r, leads us to study
numerical solutions of theories truncated at four derivatives. Rather than two
horizons we are led to the suggestion that the original horizon is replaced by
a rapid nonsingular transition from weak to strong gravity. We also consider
this possibility for the de Sitter horizon.Comment: 15 pages, 3 figures, improvements and references added, to appear in
PR
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