454 research outputs found
Note on New KLT relations
In this short note, we present two results about KLT relations discussed in
recent several papers. Our first result is the re-derivation of Mason-Skinner
MHV amplitude by applying the S_{n-3} permutation symmetric KLT relations
directly to MHV amplitude. Our second result is the equivalence proof of the
newly discovered S_{n-2} permutation symmetric KLT relations and the well-known
S_{n-3} permutation symmetric KLT relations. Although both formulas have been
shown to be correct by BCFW recursion relations, our result is the first direct
check using the regularized definition of the new formula.Comment: 15 Pages; v2: minor correction
On tree amplitudes with gluons coupled to gravitons
In this paper, we study the tree amplitudes with gluons coupled to gravitons.
We first study the relations among the mixed amplitudes. With BCFW on-shell
recursion relation, we will show the color-order reversed relation,
-decoupling relation and KK relation hold for tree amplitudes with gluons
coupled to gravitons. We then study the disk relation which expresses mixed
amplitudes by pure gluon amplitudes. More specifically we will prove the disk
relation for mixed amplitudes with gluons coupled to one graviton. Using the
disk relation and the properties of pure gluon amplitudes, the color-order
reversed relation, -decoupling relation and KK relation for mixed
amplitudes can also be proved. Finally, we give some brief discussions on
BCJ-like relation for mixed amplitudes.Comment: 33pages,no figur
Proof of Gravity and Yang-Mills Amplitude Relations
Using BCFW on-shell recursion techniques, we prove a sequence of explicit
n-point Kawai-Lewellen-Tye relations between gravity and Yang-Mills amplitudes
at tree level.Comment: 17 pages, no figures, JHE
Evidence for F(uzz) Theory
We show that in the decoupling limit of an F-theory compactification, the
internal directions of the seven-branes must wrap a non-commutative four-cycle
S. We introduce a general method for obtaining fuzzy geometric spaces via toric
geometry, and develop tools for engineering four-dimensional GUT models from
this non-commutative setup. We obtain the chiral matter content and Yukawa
couplings, and show that the theory has a finite Kaluza-Klein spectrum. The
value of 1/alpha_(GUT) is predicted to be equal to the number of fuzzy points
on the internal four-cycle S. This relation puts a non-trivial restriction on
the space of gauge theories that can arise as a limit of F-theory. By viewing
the seven-brane as tiled by D3-branes sitting at the N fuzzy points of the
geometry, we argue that this theory admits a holographic dual description in
the large N limit. We also entertain the possibility of constructing string
models with large fuzzy extra dimensions, but with a high scale for quantum
gravity.Comment: v2: 66 pages, 3 figures, references and clarifications adde
F-theory and Neutrinos: Kaluza-Klein Dilution of Flavor Hierarchy
We study minimal implementations of Majorana and Dirac neutrino scenarios in
F-theory GUT models. In both cases the mass scale of the neutrinos m_nu ~
(M_weak)^2/M_UV arises from integrating out Kaluza-Klein modes, where M_UV is
close to the GUT scale. The participation of non-holomorphic Kaluza-Klein mode
wave functions dilutes the mass hierarchy in comparison to the quark and
charged lepton sectors, in agreement with experimentally measured mass
splittings. The neutrinos are predicted to exhibit a "normal" mass hierarchy,
with masses m_3,m_2,m_1 ~ .05*(1,(alpha_GUT)^(1/2),alpha_GUT) eV. When the
interactions of the neutrino and charged lepton sectors geometrically unify,
the neutrino mixing matrix exhibits a mild hierarchical structure such that the
mixing angles theta_23 and theta_12 are large and comparable, while theta_13 is
expected to be smaller and close to the Cabibbo angle: theta_13 ~ theta_C ~
(alpha_GUT)^(1/2) ~ 0.2. This suggests that theta_13 should be near the current
experimental upper bound.Comment: v2: 83 pages, 10 figures, references adde
Inflation on the Brane with Vanishing Gravity
Many existing models of brane inflation suffer from a steep irreducible
gravitational potential between the branes that causes inflation to end too
early. Inspired by the fact that point masses in 2+1 D exert no gravitational
force, we propose a novel unwarped and non-supersymmetric setup for inflation,
consisting of 3-branes in two extra dimensions compactified on a sphere. The
size of the sphere is stabilized by a combination of a bulk cosmological
constant and a magnetic flux. Computing the 4D effective potential between
probe branes in this background, we find a non-zero contribution only from
exchange of level-1 KK modes of the graviton and radion. Identifying antipodal
points on the 2-sphere projects out these modes, eliminating entirely the
troublesome gravitational contribution to the inflationary potential.Comment: 19 pages, 11 figures, JHEP forma
Explicit BCJ Numerators from Pure Spinors
We derive local kinematic numerators for gauge theory tree amplitudes which
manifestly satisfy Jacobi identities analogous to color factors. They naturally
emerge from the low energy limit of superstring amplitudes computed with the
pure spinor formalism. The manifestation of the color--kinematics duality is a
consequence of the superstring computation involving no more than (n-2)!
kinematic factors for the full color dressed n-point amplitude. The bosonic
part of these results describe gluon scattering independent on the number of
supersymmetries and captures any N^kMHV helicity configuration after
dimensional reduction to D=4 dimensions.Comment: 32 pages, harvma
Froggatt-Nielsen models from E8 in F-theory GUTs
This paper studies F-theory SU(5) GUT models where the three generations of
the standard model come from three different curves. All the matter is taken to
come from curves intersecting at a point of enhanced E8 gauge symmetry. Giving
a vev to some of the GUT singlets naturally implements a Froggatt-Nielsen
approach to flavour structure. A scan is performed over all possible models and
the results are filtered using phenomenological constraints. We find a unique
model that fits observations of quark and lepton masses and mixing well. This
model suffers from two drawbacks: R-parity must be imposed by hand and there is
a doublet-triplet splitting problem.Comment: 42 pages; v2:journal version; v3:corrected typo in neutrino masse
Flavor Structure in F-theory Compactifications
F-theory is one of frameworks in string theory where supersymmetric grand
unification is accommodated, and all the Yukawa couplings and Majorana masses
of right-handed neutrinos are generated. Yukawa couplings of charged fermions
are generated at codimension-3 singularities, and a contribution from a given
singularity point is known to be approximately rank 1. Thus, the approximate
rank of Yukawa matrices in low-energy effective theory of generic F-theory
compactifications are minimum of either the number of generations N_gen = 3 or
the number of singularity points of certain types. If there is a geometry with
only one E_6 type point and one D_6 type point over the entire 7-brane for
SU(5) gauge fields, F-theory compactified on such a geometry would reproduce
approximately rank-1 Yukawa matrices in the real world. We found, however, that
there is no such geometry. Thus, it is a problem how to generate hierarchical
Yukawa eigenvalues in F-theory compactifications. A solution in the literature
so far is to take an appropriate factorization limit. In this article, we
propose an alternative solution to the hierarchical structure problem (which
requires to tune some parameters) by studying how zero mode wavefunctions
depend on complex structure moduli. In this solution, the N_gen x N_gen CKM
matrix is predicted to have only N_gen entries of order unity without an extra
tuning of parameters, and the lepton flavor anarchy is predicted for the lepton
mixing matrix. We also obtained a precise description of zero mode
wavefunctions near the E_6 type singularity points, where the up-type Yukawa
couplings are generated.Comment: 148 page
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