23,609 research outputs found
Free field realization of current superalgebra
We construct the free field representation of the affine currents,
energy-momentum tensor and screening currents of the first kind of the current
superalgebra uniformly for and . The energy-momentum
tensor is given by a linear combination of two Sugawara tensors associated with
the two independent quadratic Casimir elements of .Comment: Latex file, 15 page
On Atkin and Swinnerton-Dyer Congruence Relations (2)
In this paper we give an example of a noncongruence subgroup whose
three-dimensional space of cusp forms of weight 3 has the following properties.
For each of the four residue classes of odd primes modulo 8 there is a basis
whose Fourier coefficients at infinity satisfy a three-term Atkin and
Swinnerton-Dyer congruence relation, which is the -adic analogue of the
three-term recursion satisfied by the coefficients of classical Hecke eigen
forms. We also show that there is an automorphic -function over
whose local factors agree with those of the -adic Scholl representations
attached to the space of noncongruence cusp forms.Comment: Last version, to appear on Math Annale
Triton-3He relative and differential flows and the high density behavior of nuclear symmetry energy
Using a transport model coupled with a phase-space coalescence after-burner
we study the triton-3He relative and differential transverse flows in
semi-central 132Sn+124Sn reactions at a beam energy of 400 MeV/nucleon. We find
that the triton-3He pairs carry interesting information about the density
dependence of the nuclear symmetry energy. The t-3He relative flow can be used
as a particularly powerful probe of the high-density behavior of the nuclear
symmetry energy.Comment: 6 pages, 2 figures, Proceeding of The International Workshop on
Nuclear Dynamics in Heavy-Ion Reactions and the Symmetry Energ
On the exactness of soft theorems
Soft behaviours of S-matrix for massless theories reflect the underlying
symmetry principle that enforces its masslessness. As an expansion in soft
momenta, sub-leading soft theorems can arise either due to (I) unique structure
of the fundamental vertex or (II) presence of enhanced broken-symmetries. While
the former is expected to be modified by infrared or ultraviolet divergences,
the latter should remain exact to all orders in perturbation theory. Using
current algebra, we clarify such distinction for spontaneously broken (super)
Poincar\'e and (super) conformal symmetry. We compute the UV divergences of
DBI, conformal DBI, and A-V theory to verify the exactness of type (II) soft
theorems, while type (I) are shown to be broken and the soft-modifying
higher-dimensional operators are identified. As further evidence for the
exactness of type (II) soft theorems, we consider the alpha' expansion of both
super and bosonic open strings amplitudes, and verify the validity of the
translation symmetry breaking soft-theorems up to O(alpha'^6). Thus the
massless S-matrix of string theory "knows" about the presence of D-branes.Comment: 35 pages. Additional mathematica note book with the UV-divergenece of
the 6-point amplitude in AV/KS theor
Characterizations of Pseudo-Codewords of LDPC Codes
An important property of high-performance, low complexity codes is the
existence of highly efficient algorithms for their decoding. Many of the most
efficient, recent graph-based algorithms, e.g. message passing algorithms and
decoding based on linear programming, crucially depend on the efficient
representation of a code in a graphical model. In order to understand the
performance of these algorithms, we argue for the characterization of codes in
terms of a so called fundamental cone in Euclidean space which is a function of
a given parity check matrix of a code, rather than of the code itself. We give
a number of properties of this fundamental cone derived from its connection to
unramified covers of the graphical models on which the decoding algorithms
operate. For the class of cycle codes, these developments naturally lead to a
characterization of the fundamental polytope as the Newton polytope of the
Hashimoto edge zeta function of the underlying graph.Comment: Submitted, August 200
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