24,887 research outputs found
Non-renormalization for the Liouville wave function
Using an exact functional method, within the framework of the gradient
expansion for the Liouville effective action, we show that the kinetic term for
the Liouville field is not renormalized.Comment: 13 pages Latex, no figure
Path integral quantization of scalar fluctuations above a kink
We quantize scalar fluctuations in 1+1 dimensions above a classical
background kink. The properties of the effective action for the corresponding
classical field are studied with an exact functional method, alternative to
exact Wilsonian renormalization, where the running parameter is a bare mass,
and the regulator of the quantum theory is fixed. We extend this approach, in
an appendix, to a Yukawa interaction in higher dimension.Comment: Comments adde
Maxwell Construction for Scalar Field Theories with Spontaneous Symmetry Breaking
Using a non-perturbative approximation for the partition function of a
complex scalar model, which features spontaneous symmetry breaking, we
explicitly derive the flattening of the effective potential in the region
limited by the minima of the bare potential. This flattening occurs in the
limit of infinite volume, and is a consequence of the summation over the
continuous set of saddle points which dominate the partition function. We also
prove the convexity of the effective potential and generalize the Maxwell
Construction for scalar theories with O(N) symmetry. Finally, we discuss why
the flattening of the effective potential cannot occur in the Abelian Higgs
theory.Comment: 22 pages, 2 figures, comments and references adde
On higher-order corrections in a four-fermion Lifshitz model
We study a flavour-violating four-fermion interaction in the Lifshitz
context, in 3+1 dimensions and with a critical exponent z=3. This model is
renormalizable, and features dynamical mass generation, as well as asymptotic
freedom. At one-loop, it is only logarithmically divergent, but the superficial
degree of divergence of the two-point functions is 3. We calculate the two-loop
corrections to the propagators, and show that, at this order, the
Lorentz-violating corrections to the IR dispersion relation are quadratic in
the cut off. Furthermore, these corrections are too important to represent a
physical effect. As a consequence, the predictive power of the model in terms
of Lorentz-violating effects in the propagation of particles is limited.Comment: 20 pages, 3 figures, comments adde
Non-Perturbative Formulation of Time-Dependent String Solutions
We formulate here a new world-sheet renormalization-group technique for the
bosonic string, which is non-perturbative in the Regge slope alpha' and based
on a functional method for controlling the quantum fluctuations, whose
magnitudes are scaled by the value of alpha'. Using this technique we exhibit,
in addition to the well-known linear-dilaton cosmology, a new, non-perturbative
time-dependent background solution. Using the reparametrization invariance of
the string S-matrix, we demonstrate that this solution is conformally invariant
to alpha', and we give a heuristic inductive argument that conformal invariance
can be maintained to all orders in alpha'. This new time-dependent string
solution may be applicable to primordial cosmology or to the exit from
linear-dilaton cosmology at large times
Quantization leading to a natural flattening of the axion potential
Starting from the general cosine form for the axion effective potential, we
quantize the axion and show that the result is described by a naturally flat
potential, if interactions with other particles are not considered. This
feature therefore restores the would-be Goldstone-boson nature of the axion,
and we calculate the corresponding vacuum energy density, which does not need
to be too large by orders of magnitude compared to Dark Energy
Scalable Successive-Cancellation Hardware Decoder for Polar Codes
Polar codes, discovered by Ar{\i}kan, are the first error-correcting codes
with an explicit construction to provably achieve channel capacity,
asymptotically. However, their error-correction performance at finite lengths
tends to be lower than existing capacity-approaching schemes. Using the
successive-cancellation algorithm, polar decoders can be designed for very long
codes, with low hardware complexity, leveraging the regular structure of such
codes. We present an architecture and an implementation of a scalable hardware
decoder based on this algorithm. This design is shown to scale to code lengths
of up to N = 2^20 on an Altera Stratix IV FPGA, limited almost exclusively by
the amount of available SRAM
Do Three Dimensions tell us Anything about a Theory of Everything?
It has been conjectured that four-dimensional N=8 supergravity may provide a
suitable framework for a `Theory of Everything', if its composite SU(8) gauge
fields become dynamical. We point out that supersymmetric three-dimensional
coset field theories motivated by lattice models provide toy laboratories for
aspects of this conjecture. They feature dynamical composite supermultiplets
made of constituent holons and spinons. We show how these models may be
extended to include N=1 and N=2 supersymmetry, enabling dynamical conjectures
to be verified more rigorously. We point out some special features of these
three-dimensional models, and mention open questions about their relevance to
the dynamics of N=8 supergravity.Comment: 20 pages Latex, 2 eps figure
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