1,158 research outputs found
Pipelined Two-Operand Modular Adders
Pipelined two-operand modular adder (TOMA) is one of basic components used in digital signal processing (DSP) systems that use the residue number system (RNS). Such modular adders are used in binary/residue and residue/binary converters, residue multipliers and scalers as well as within residue processing channels. The design of pipelined TOMAs is usually obtained by inserting an appriopriate number of latch layers inside a nonpipelined TOMA structure. Hence their area is also determined by the number of latches and the delay by the number of latch layers. In this paper we propose a new pipelined TOMA that is based on a new TOMA, that has the smaller area and smaller delay than other known structures. Comparisons are made using data from the very large scale of integration (VLSI) standard cell library
The Geometry of Gauged Linear Sigma Model Correlation Functions
Applying advances in exact computations of supersymmetric gauge theories, we
study the structure of correlation functions in two-dimensional N=(2,2) Abelian
and non-Abelian gauge theories. We determine universal relations among
correlation functions, which yield differential equations governing the
dependence of the gauge theory ground state on the Fayet-Iliopoulos parameters
of the gauge theory. For gauge theories with a non-trivial infrared N=(2,2)
superconformal fixed point, these differential equations become the
Picard-Fuchs operators governing the moduli-dependent vacuum ground state in a
Hilbert space interpretation. For gauge theories with geometric target spaces,
a quadratic expression in the Givental I-function generates the analyzed
correlators. This gives a geometric interpretation for the correlators, their
relations, and the differential equations. For classes of Calabi-Yau target
spaces, such as threefolds with up to two Kahler moduli and fourfolds with a
single Kahler modulus, we give general and universally applicable expressions
for Picard-Fuchs operators in terms of correlators. We illustrate our results
with representative examples of two-dimensional N=(2,2) gauge theories.Comment: 76 pages, v2: references added and minor improvement
Higher dimensional 3-adic CM construction
We find equations for the higher dimensional analogue of the modular curve
X_0(3) using Mumford's algebraic formalism of algebraic theta functions. As a
consequence, we derive a method for the construction of genus 2 hyperelliptic
curves over small degree number fields whose Jacobian has complex
multiplication and good ordinary reduction at the prime 3. We prove the
existence of a quasi-quadratic time algorithm for computing a canonical lift in
characteristic 3 based on these equations, with a detailed description of our
method in genus 1 and 2.Comment: 23 pages; major revie
CFT and topological recursion
We study the quasiclassical expansion associated with a complex curve. In a
more specific context this is the 1/N expansion in U(N)-invariant matrix
integrals. We compare two approaches, the CFT approach and the topological
recursion, and show their equivalence. The CFT approach reformulates the
problem in terms of a conformal field theory on a Riemann surface, while the
topological recursion is based on a recurrence equation for the observables
representing symplectic invariants on the complex curve. The two approaches
lead to two different graph expansions, one of which can be obtained as a
partial resummation of the other.Comment: Minor correction
Matrix Factorizations, Minimal Models and Massey Products
We present a method to compute the full non-linear deformations of matrix
factorizations for ADE minimal models. This method is based on the calculation
of higher products in the cohomology, called Massey products. The algorithm
yields a polynomial ring whose vanishing relations encode the obstructions of
the deformations of the D-branes characterized by these matrix factorizations.
This coincides with the critical locus of the effective superpotential which
can be computed by integrating these relations. Our results for the effective
superpotential are in agreement with those obtained from solving the A-infinity
relations. We point out a relation to the superpotentials of Kazama-Suzuki
models. We will illustrate our findings by various examples, putting emphasis
on the E_6 minimal model.Comment: 32 pages, v2: typos corrected, v3: additional comments concerning the
bulk-boundary crossing constraint, some small clarifications, typo
SQCD: A Geometric Apercu
We take new algebraic and geometric perspectives on the old subject of SQCD.
We count chiral gauge invariant operators using generating functions, or
Hilbert series, derived from the plethystic programme and the Molien-Weyl
formula. Using the character expansion technique, we also see how the global
symmetries are encoded in the generating functions. Equipped with these methods
and techniques of algorithmic algebraic geometry, we obtain the character
expansions for theories with arbitrary numbers of colours and flavours.
Moreover, computational algebraic geometry allows us to systematically study
the classical vacuum moduli space of SQCD and investigate such structures as
its irreducible components, degree and syzygies. We find the vacuum manifolds
of SQCD to be affine Calabi-Yau cones over weighted projective varieties.Comment: 49 pages, 1 figur
The WDVV equations in pure Seiberg-Witten theory
We review the relationship between pure four-dimensional Seiberg–Witten theory and the periodic Toda chain. We discuss the definition of the prepotential and give two proofs that it satisfies the generalized Witten–Dijkgraaf–Verlinde–Verlinde equations. A number of steps in the definitions and proofs that is missing in the literature is supplied
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