3,541 research outputs found
BPS Saturated Amplitudes and Non-perturbative String Theory
The study of the special F^4 and R^4 in the effective action for the
Spin(32)/Z_2 and type II strings sheds some light on D-brane calculus and on
instanton contribution counting. The D-instanton case is discussed separately.Comment: latex 4 pages, crckapb style used. Cargese 1997 Gong show.v2 English
corrected. v3 correction correcte
A geometric proof of the upper bound on the size of partial spreads in H(4n+1, q²)
We give a geometric proof of the upper bound of q(2n+1) + 1 on the size of partial spreads in the polar space H(4n + 1, q(2)). This bound is tight and has already been proved in an algebraic way. Our alternative proof also yields a characterization of the partial spreads of maximum size in H(4n + 1, q(2))
The critical ultraviolet behaviour of N=8 supergravity amplitudes
We analyze the critical ultraviolet behaviour of the four-graviton amplitude
in N=8 supergravity to all order in perturbation. We use the
Bern-Carrasco-Johansson diagrammatic expansion for N=8 supergravity multiloop
amplitudes, where numerator factors are squares of the Lorentz factor of N=4
super-Yang-Mills amplitudes, and the analysis of the critical ultraviolet
behaviour of the multiloop four-gluon amplitudes in the single- and
double-trace sectors. We argue this implies that the superficial ultraviolet
behaviour of the four-graviton N=8 amplitudes from four-loop order is
determined by the factorization the k^8 R^4 operator. This leads to a
seven-loop logarithmic divergence in the four-graviton amplitude in four
dimensions.Comment: latex. 5 pages. v2: Added references and minor change
The physics and the mixed Hodge structure of Feynman integrals
This expository text is an invitation to the relation between quantum field
theory Feynman integrals and periods. We first describe the relation between
the Feynman parametrization of loop amplitudes and world-line methods, by
explaining that the first Symanzik polynomial is the determinant of the period
matrix of the graph, and the second Symanzik polynomial is expressed in terms
of world-line Green's functions. We then review the relation between Feynman
graphs and variations of mixed Hodge structures. Finally, we provide an
algorithm for generating the Picard-Fuchs equation satisfied by the all equal
mass banana graphs in a two-dimensional space-time to all loop orders.Comment: v2: 34 pages, 5 figures. Minor changes. References added. String-math
2013 proceeding contributio
A Feynman integral via higher normal functions
We study the Feynman integral for the three-banana graph defined as the
scalar two-point self-energy at three-loop order. The Feynman integral is
evaluated for all identical internal masses in two space-time dimensions. Two
calculations are given for the Feynman integral; one based on an interpretation
of the integral as an inhomogeneous solution of a classical Picard-Fuchs
differential equation, and the other using arithmetic algebraic geometry,
motivic cohomology, and Eisenstein series. Both methods use the rather special
fact that the Feynman integral is a family of regulator periods associated to a
family of K3 surfaces. We show that the integral is given by a sum of elliptic
trilogarithms evaluated at sixth roots of unity. This elliptic trilogarithm
value is related to the regulator of a class in the motivic cohomology of the
K3 family. We prove a conjecture by David Broadhurst that at a special
kinematical point the Feynman integral is given by a critical value of the
Hasse-Weil L-function of the K3 surface. This result is shown to be a
particular case of Deligne's conjectures relating values of L-functions inside
the critical strip to periods.Comment: Latex. 70 pages. 3 figures. v3: minor changes and clarifications.
Version to appear in Compositio Mathematic
Localized gravity in non-compact superstring models
We discuss a string-theory-derived mechanism for localized gravity, which
produces a deviation from Newton's law of gravitation at cosmological
distances. This mechanism can be realized for general non-compact Calabi-Yau
manifolds, orbifolds and orientifolds. After discussing the cross-over scale
and the thickness in these models we show that the localized higher derivative
terms can be safely neglected at observable distances. We conclude by some
observations on the massless open string spectrum for the orientifold models.Comment: 12 Pages. Based on some unpublished work presented at Quarks-2004,
Pushkinskie Gory, Russia, May 24-3
The elliptic dilogarithm for the sunset graph
We study the sunset graph defined as the scalar two-point self-energy at
two-loop order. We evaluate the sunset integral for all identical internal
masses in two dimensions. We give two calculations for the sunset amplitude;
one based on an interpretation of the amplitude as an inhomogeneous solution of
a classical Picard-Fuchs differential equation, and the other using arithmetic
algebraic geometry, motivic cohomology, and Eisenstein series. Both methods use
the rather special fact that the amplitude in this case is a family of periods
associated to the universal family of elliptic curves over the modular curve
X_1(6). We show that the integral is given by an elliptic dilogarithm evaluated
at a sixth root of unity modulo periods. We explain as well how this elliptic
dilogarithm value is related to the regulator of a class in the motivic
cohomology of the universal elliptic family.Comment: 3 figures, 43 pages. v2: minor corrections. version to be published
in The Journal of Number Theor
- …