scholarly journals Homotopy operators for the variational bicomplex, representations of the Euler-Lagrange complex, and the Helmholtz-Sonin conditions

2009 ◽  
Vol 30 (2) ◽  
pp. 107-123 ◽  
Author(s):  
M. Crampin ◽  
D. J. Saunders
Keyword(s):  
Variational Bicomplex ◽  
Homotopy Operators

ONE-LOOP VACUUM ENERGY AT THE TACHYON VACUUM

2013 ◽  
Vol 21 ◽  
pp. 157-158
Author(s):  
SHOKO INATOMI
Keyword(s):  
Field Theory ◽  
Quantum Theory ◽  
String Field Theory ◽  
Vacuum Energy ◽  
Open String ◽  
Brst Operator ◽  
Identity Based ◽  
Homotopy Operators

We consider one-loop vacuum energy at the tachyon vacuum in cubic bosonic open string field theory. The BRST operator Ql in the theory around an identity-based solution is believed to represent a kinetic operator at the tachyon vacuum. Using homotopy operators for Ql, we find that one-loop vacuum energy at the tachyon vacuum is independent of moduli such as interbrane distances. This result can be interpreted as support for the annihilation of D-branes at the tachyon vacuum even in the quantum theory.

scholarly journals Homotopy Operators and One-Loop Vacuum Energy at the Tachyon Vacuum

2011 ◽  
Vol 126 (6) ◽  
pp. 1077-1089 ◽  
Author(s):  
S. Inatomi ◽  
I. Kishimoto ◽  
T. Takahashi
Keyword(s):  
Vacuum Energy ◽  
Homotopy Operators

scholarly journals Homotopy operators and identity-based solutions in cubic superstring field theory

2011 ◽  
Vol 2011 (10) ◽  
Author(s):  
Shoko Inatomi ◽  
Isao Kishimoto ◽  
Tomohiko Takahashi
Keyword(s):  
Field Theory ◽  
Identity Based ◽  
Homotopy Operators

LOCAL COHOMOLOGY AND THE VARIATIONAL BICOMPLEX

2008 ◽  
Vol 05 (04) ◽  
pp. 587-604 ◽  
Author(s):  
ROBERTO FERREIRO PÉREZ
Keyword(s):  
Principal Bundle ◽  
Local Cohomology ◽  
Differential Forms ◽  
Riemannian Metrics ◽  
Jet Bundle ◽  
Variational Bicomplex

The differential forms on the jet bundle J∞E of a bundle E → M over a compact n-manifold M of degree greater than n determine differential forms on the space Γ(E) of sections of E. The forms obtained in this way are called local forms on Γ(E), and its cohomology is called the local cohomology of Γ(E). More generally, if a group [Formula: see text] acts on E, we can define the local [Formula: see text]-invariant cohomology. The local cohomology is computed in terms of the cohomology of the jet bundle by means of the variational bicomplex theory. A similar result is obtained for the local [Formula: see text]-invariant cohomology. Using these results and the techniques for the computation of the cohomology of invariant variational bicomplexes in terms of relative Gelfand–Fuchs cohomology introduced in [4], we construct non trivial local cohomology classes in the important cases of Riemannian metrics with the action of diffeomorphisms, and connections on a principal bundle with the action of automorphisms.

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