7,096 research outputs found
Relative quasimaps and mirror formulae
We construct and study the theory of relative quasimaps in genus zero, in the
spirit of A. Gathmann. When is a smooth toric variety and is a very
ample hypersurface in we produce a virtual class on the moduli space of
relative quasimaps to which can be used to define relative quasimap
invariants of the pair. We obtain a recursion formula which expresses each
relative invariant in terms of invariants of lower tangency, and apply this
formula to derive a quantum Lefschetz theorem for quasimaps, expressing the
restricted quasimap invariants of in terms of those of . Finally, we
show that the relative -function of Fan-Tseng-You coincides with a natural
generating function for relative quasimap invariants, providing
mirror-symmetric motivation for the theory.Comment: 32 pages, 1 figure; comments welcome. v2: added a stronger version of
the quantum Lefschetz theorem. v3: additional section exploring applications
to relative mirror symmetry; new title and introductio
Note on Identities Inspired by New Soft Theorems
The new soft theorems, for both gravity and gauge amplitudes, have inspired a
number of works, including the discovery of new identities related to
amplitudes. In this note, we present the proof and discussion for two sets of
identities. The first set includes an identity involving the half-soft function
which had been used in the soft theorem for one-loop rational gravity
amplitudes, and another simpler identity as its byproduct. The second set
includes two identities involving the KLT momentum kernel, as the consistency
conditions of the KLT relation plus soft theorems for both gravity and gauge
amplitudes. We use the CHY formulation to prove the first identity, and
transform the second one into a convenient form for future discussion.Comment: 17 page
On the Classification of Residues of the Grassmannian
We study leading singularities of scattering amplitudes which are obtained as
residues of an integral over a Grassmannian manifold. We recursively do the
transformation from twistors to momentum twistors and obtain an iterative
formula for Yangian invariants that involves a succession of dualized twistor
variables. This turns out to be useful in addressing the problem of classifying
the residues of the Grassmannian. The iterative formula leads naturally to new
coordinates on the Grassmannian in terms of which both composite and
non-composite residues appear on an equal footing. We write down residue
theorems in these new variables and classify the independent residues for some
simple examples. These variables also explicitly exhibit the distinct solutions
one expects to find for a given set of vanishing minors from Schubert calculus.Comment: 20 page
Functional programming with bananas, lenses, envelopes and barbed wire
We develop a calculus for lazy functional programming based on recursion operators associated with data type definitions. For these operators we derive various algebraic laws that are useful in deriving and manipulating programs. We shall show that all example functions in Bird and Wadler's Introduction to Functional Programming can be expressed using these operators
New Moduli Spaces from String Background Independence Consistency Conditions
In string field theory an infinitesimal background deformation is implemented
as a canonical transformation whose hamiltonian function is defined by moduli
spaces of punctured Riemann surfaces having one special puncture. We show that
the consistency conditions associated to the commutator of two deformations are
implemented by virtue of the existence of moduli spaces of punctured surfaces
with two special punctures. The spaces are antisymmetric under the exchange of
the special punctures, and satisfy recursion relations relating them to moduli
spaces with one special puncture and to string vertices. We develop the theory
of moduli spaces of surfaces with arbitrary number of special punctures and
indicate their relevance to the construction of a string field theory that
makes no reference to a conformal background. Our results also imply a partial
antibracket cohomology theorem for the string action.Comment: 42 pages, requires phyzzx, BoxedEPS, 6 ps figure
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