589 research outputs found
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
Induced Gravity II: Grand Unification
As an illustration of a renormalizable, asymptotically-free model of induced
gravity, we consider an gauge theory interacting with a real scalar
multiplet in the adjoint representation. We show that dimensional transmutation
can occur, spontaneously breaking to while
inducing the Planck mass and a positive cosmological constant, all proportional
to the same scale . All mass ratios are functions of the values of coupling
constants at that scale. Below this scale (at which the Big Bang may occur),
the model takes the usual form of Einstein-Hilbert gravity in de Sitter space
plus calculable corrections. We show that there exist regions of parameter
space in which the breaking results in a local minimum of the effective action,
and a {\bf positive} dilaton from two-loop corrections
associated with the conformal anomaly. Furthermore, unlike the singlet case we
considered previously, some minima lie within the basin of attraction of the
ultraviolet fixed point. Moreover, the asymptotic behavior of the coupling
constants also lie within the range of convergence of the Euclidean path
integral, so there is hope that there will be candidates for sensible vacua.
Although open questions remain concerning unitarity of all such renormalizable
models of gravity, it is not obvious that, in curved backgrounds such as those
considered here, unitarity is violated. In any case, any violation that may
remain will be suppressed by inverse powers of the reduced Planck mass.Comment: 44 pages, 5 figures, 2 tables. v2 has new discussion concerning
stability of SSB plus related appendix. Additional references added. v3 is
version to be published; contains minor revision
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
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