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Instantons and SL(2,R) Symmetry in Type IIB Supergravity
We discuss the relation between the dual formulations of Type IIB
supergravity emphasizing the differences between Lorentz and Euclidean
signature. We demonstrate how the SL(2,R) symmetry of the usual action is
manifested in the solution of the equations of motion with Euclidean signature
for the dual theory.Comment: 4 pages, no figure
Effective Beta-Functions for Effective Field Theory
We consider the problem of determining the beta-functions for any reduced
effective field theory. Even though not all the Green's functions of a reduced
effective field theory are renormalizable, unlike the full effective field
theory, certain effective beta- functions for the reduced set of couplings may
be calculated without having to introduce vertices in the Feynman rules for
redundant operators. These effective beta-functions suffice to apply the
renormalization group equation to any transition amplitude (i.e., S- matrix
element), thereby rendering reduced effective field theories no more cumbersome
than traditionally renormalizable field theories. These effective
beta-functions may equally be regarded as the running of couplings for a
particular redefinition of the fields.Comment: 13 pages, LaTeX (requires JHEP class). Version 3: additional
references and a slight expansion of Sections 3 and 5. No substantive change
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