226 research outputs found
Some Issues In The Loop Variable Approach to Open Strings and an Extension to Closed Strings
Some issues in the loop variable renormalization group approach to gauge
invariant equations for the free fields of the open string are discussed. It
had been shown in an earlier paper that this leads to a simple form of the
gauge transformation law. We discuss in some detail some of the curious
features encountered there. The theory looks a little like a massless theory in
one higher dimension that can be dimensionally reduced to give a massive
theory. We discuss the origin of some constraints that are needed for gauge
invariance and also for reducing the set of fields to that of standard string
theory. The mechanism of gauge invariance and the connection with the Virasoro
algebra is a little different from the usual story and is discussed. It is also
shown that these results can be extended in a straightforward manner to closed
strings.Comment: 24 page
Loop Variables and Gauge Invariant Exact Renormalization Group Equations for (Open) String Theory
An exact renormalization group equation is written down for the world sheet
theory describing the bosonic open string in general backgrounds. Loop variable
techniques are used to make the equation gauge invariant. This is worked out
explicitly up to level 3. The equation is quadratic in the fields and can be
viewed as a proposal for a string field theory equation. As in the earlier loop
variable approach, the theory has one extra space dimension and mass is
obtained by dimensional reduction. Being based on the sigma model RG, it is
background independent.
It is intriguing that in contrast to BRST string field theory, the gauge
transformations are not modified by the interactions up to the level
calculated. The interactions can be written in terms of gauge invariant field
strengths for the massive higher spin fields and the non zero mass is essential
for this. This is reminiscent of Abelian Born-Infeld action (along with
derivative corrections) for the massless vector field, which is also written in
terms of the field strength.Comment: Latex file, 40 pages.Some typos corrected and cosmetic change
Proper Time Formalism, Gauge Invariance and the Effects of a Finite World Sheet Cutoff in String Theory
We discuss the issue of going off-shell in the proper time formalism. This is
done by keeping a finite world sheet cutoff. We construct one example of an
off-shell covariant Klein Gordon type interaction. For a suitable choice of the
gauge transformation of the scalar field, gauge invariance is maintained off
mass shell. However at second order in the gauge field interaction, one finds
that (U(1)) gauge invariance is violated due to the finite cutoff.
Interestingly, we find, to lowest order, that by adding a massive mode with
appropriate gauge transformation laws to the sigma model background, one can
restore gauge invariance. The gauge transformation law is found to be
consistent, to the order calculated, with what one expects from the interacting
equation of motion of the massive field. We also extend some previous
discussion on applying the proper time formalism for propagating gauge
particles, to the interacting (i.e. Yang Mills) case.Comment: 24 pages, Latex file. (This is a revised version, to appear in Int.
J. of Mod. Phys. Section 2 has been extensively revised. Minor revisions in
the other sections
The Proper Time Equation and the Zamolodchikov Metric
The connection between the proper time equation and the Zamolodchikov metric
is discussed. The connection is two-fold: First, as already known, the proper
time equation is the product of the Zamolodchikov metric and the
renormalization group beta function. Second, the condition that the two-point
function is the Zamolodchikov metric, implies the proper time equation. We
study the massless vector of the open string in detail. In the exactly
calculable case of a uniform electromgnetic field strength we recover the
Born-Infeld equation. We describe the systematics of the perturbative
evaluation of the gauge invariant proper time equation for the massless vector
field. The method is valid for non-uniform fields and gives results that are
exact to all orders in derivatives. As a non trivial check, we show that in the
limit of uniform fields it reproduces the lowest order Born-Infeld equation.Comment: Latex file, 29 pages, A couple of minor typos corrected. Final
version, to appear in Int. Journal of Mod. Phys.
Loop Variables and Gauge Invariant Interactions of Massive Modes in String Theory
The loop variable approach used earlier to obtain free equations of motion
for the massive modes of the open string, is generalized to include interaction
terms. These terms, which are polynomial, involve only modes of strictly lower
mass. Considerations based on operator product expansions suggest that these
equations are particular truncations of the full string equations. The method
involves broadening the loop to a band of finite thickness that describes all
the different interacting strings. Interestingly, in terms of these variables,
the theory appears non-interacting.Comment: Latex file, 19 page
Fundamental Strings and D-strings in the IIB Matrix Model
The matrix model for IIB Superstring proposed by Ishibashi, Kawai, Kitazawa
and Tsuchiya is investigated. Consideration of planar and non-planar diagrams
suggests that the large N perturbative expansion is consistent with the double
scaling limit proposed by the above authors. We write down a Wilson loop that
can be interpreted as a fundamental string vertex operator. The one point
tadpole in the presence of a D-string has the right form and this can be viewed
as a matrix model derivation of the boundary conditions that define a D-string.
We also argue that if world sheet coordinates and are
introduced for the fundamental string, then the conjugate variable
and can be interpreted as the D-string world
sheet coordinates. In this way the duality group of the IIB
superstring becomes identified with the symplectic group acting on ().Comment: 21 pages, Latex file. Two references added and two figures include
Loop Variables and Gauge Invariant Interactions - I
We describe a method of writing down interacting equations for all the modes
of the bosonic open string. It is a generalization of the loop variable
approach that was used earlier for the free, and lowest order interacting
cases. The generalization involves, as before, the introduction of a parameter
to label the different strings involved in an interaction. The interacting
string has thus becomes a ``band'' of finite width. The interaction equations
expressed in terms of loop variables, has a simple invariance that is exact
even off shell. A consistent definition of space-time fields requires the
fields to be functions of all the infinite number of gauge coordinates (in
addition to space time coordinates). The theory is formulated in one higher
dimension, where the modes appear massless. The dimensional reduction that is
needed to make contact with string theory (which has been discussed earlier for
the free case) is not discussed here.Comment: 40 pages, Latex. Revised version: some typos corrected. Final version
to appear in Int. J. of Mod. Phys.
Proper Time Formalism and Gauge Invariance in Open String Interactions
The issue of gauge invariances in the sigma model formalism is discussed at
the free and interacting level. The problem of deriving gauge invariant
interacting equations can be addressed using the proper time formalism. This
formalism is discussed, both for point particles and strings. The covariant
Klein Gordon equation arises in a geometric way from the boundary terms. This
formalism is similar to the background independent open string formalism
introduced by Witten.Comment: 19 page
- …