4 research outputs found
Enumerative geometry of Calabi-Yau 4-folds
Gromov-Witten theory is used to define an enumerative geometry of curves in
Calabi-Yau 4-folds. The main technique is to find exact solutions to moving
multiple cover integrals. The resulting invariants are analogous to the BPS
counts of Gopakumar and Vafa for Calabi-Yau 3-folds. We conjecture the 4-fold
invariants to be integers and expect a sheaf theoretic explanation.
Several local Calabi-Yau 4-folds are solved exactly. Compact cases, including
the sextic Calabi-Yau in CP5, are also studied. A complete solution of the
Gromov-Witten theory of the sextic is conjecturally obtained by the holomorphic
anomaly equation.Comment: 44 page
An Updated Description of Heavy-Hadron Interactions in Geant-4
Exotic stable massive particles (SMP) are proposed in a number of scenarios
of physics beyond the Standard Model. It is important that LHC experiments are
able both to detect and extract the quantum numbers of any SMP with masses
around the TeV scale. To do this, an understanding of the interactions of SMPs
in matter is required. In this paper a Regge-based model of R-hadron scattering
is extended and implemented in Geant-4. In addition, the implications of
-hadron scattering for collider searches are discussed
The ultra-violet question in maximally supersymmetric field theories
We discuss various approaches to the problem of determining which
supersymmetric invariants are permitted as counterterms in maximally
supersymmetric super Yang--Mills and supergravity theories in various
dimensions. We review the superspace non-renormalisation theorems based on
conventional, light-cone, harmonic and certain non-Lorentz covariant
superspaces, and we write down explicitly the relevant invariants. While the
first two types of superspace admit the possibility of one-half BPS
counterterms, of the form and respectively, the last two do not.
This suggests that UV divergences begin with one-quarter BPS counterterms, i.e.
and , and this is supported by an entirely different
approach based on algebraic renormalisation. The algebraic formalism is
discussed for non-renormalisable theories and it is shown how the allowable
supersymmetric counterterms can be determined via cohomological methods. These
results are in agreement with all the explicit computations that have been
carried out to date. In particular, they suggest that maximal supergravity is
likely to diverge at four loops in D=5 and at five loops in D=4, unless other
infinity suppression mechanisms not involving supersymmetry or gauge invariance
are at work.Comment: 56 pages, 1 figure, uses youngtab.sty. Contribution to the
proceedings of the W.E. Heraeus Workhop "Quantum Gravity: Challenges and
Perspectives", Bad Honnef, 14-16 April 2008. References and clarifying
comments adde