1. Off-shell Formulation of Supersymmetric Field Theories
Victor Alexandrov
Moscow State University
Erice,
Based on the work by
V. Alexandrov, D. Krotov, A. Losev, V. Lysov.

2. Statements Statements:
Integrating out the complement to cohomologies H(Q)
Statements:
a) All effective theories are on-shell supersymmetric
b) The fundamental theory
is the off-shell version
of its effective theory
V. Alexandrov sep-2006, Erice

3. Idea Our case Conventional case Integrating out D-terms Superfield
Calculation of
effective
action
Integrating out
D-terms
i.e. integrating out fields,
which are not cohomologies
Superfield
formalism
Lambda-theta
formalism
- odd
- odd
- even
V. Alexandrov sep-2006, Erice

4. Batalin – Vilkovisky formalism
Is the most general formalism to quantize gauge theories
V. Alexandrov sep-2006, Erice

5. Batalin – Vilkovisky formalism
BV – equation for
General solution of this equation linear in BV-antifields
structure
constants
symmetry
transformations
classical action
ghosts and
antighosts for
parameters of
symmetry
transformation
Under 2 conditions:
V. Alexandrov sep-2006, Erice

6. SUSY Quantum Mechanics
The algebra of supersymmetry
Off-shell invariant action
- is ghost for supersymmetry
- is ghost for time translations
Integrating out D-terms: obtain on-shell invariant action
Terms of such structure show that
symmetry of the off-shell theory becomes on-shell.
V. Alexandrov sep-2006, Erice

7. Conclusion
All effective theories which can be obtained using the described procedure are on-shell supersimmetric.
is off-shell version of all these effective theories.
N=1, D= 10 SUSY Yang-Mills
By now
certain 2-d gauge model with matter
To be continued…
V. Alexandrov sep-2006, Erice