Universality of nonperturbative effects inc< 1 noncritical string theory

Abstract

Nonperturbative effects in c < 1 noncritical string theory are studied using the two-matrix model. Such effects are known to have the form fixed by the string equations but the numerical coefficients have not been known so far. Using the method proposed recently, we show that it is possible to determine the coefficients for (p, q) string theory. We find that they are indeed finite in the double scaling limit and universal in the sense that they do not depend on the detailed structure of the potential of the two-matrix model.

Tduality of the Zamolodchikov-Zamolodchikov brane

“…Therefore, if we interpret one of f 1 and f 2 as a quantity of the original model and the other as that of the dual model, as long as C 1 or C 2 is nonzero, the dual theory has a different nonperturbative effect from that in the original theory. It is known that the nonperturbative effects in the original theory itself take the form (2.16) [3,7], so the dual theory must also have nonperturbative effects of the same form (up to the overall constants). We will see that this is indeed the case by computing the nonperturbative effects in the dual theory directly from the matrix model (2.7).…”

“…However, it is shown in [4,7] that, if we compute these coefficients in the c < 1 noncritical string theory directly from a matrix model, they turn out to be unique and universal in the sense that they do not depend on details of a potential in the matrix model. Thus, it is interesting to examine whether this is also the case with the nonperturbative effects in the dual c = 1/2 string theory and whether they agree with those in the original theory.…”

“…Thus, it is interesting to examine whether this is also the case with the nonperturbative effects in the dual c = 1/2 string theory and whether they agree with those in the original theory. Moreover, since the nonperturbative effects are computed from certain disk and cylinder amplitudes [4,7], it will be possible to find out the T-duality at the nonperturbative level from the knowledge of the T-dual relation of the disk and cylinder amplitudes. It is expected that the analysis reveals the existence of large universality including T-duality for nonperturbative effects in string theory, or for string theory itself.…”

“…However, as noticed above, in this case we cannot trust the form of V (0) eff (x, y) given in (3.18). This kind of saddle point first appears in the dual model, not seen in the case of the original model [3,7]. In order to resolve this problem, we consider performing the Y -integration first in the partition function and then calculating instanton effects from isolated eigenvalues in the resulting one-matrix model for X.…”

“…From this point of view, it is quite intriguing to examine how nonperturbative effects are transformed under the T-duality in a possible nonperturbative framework of string theory. As such a framework, the noncritical string theory provides a useful toy model, because it can be formulated nonperturbatively by matrix models and their nonperturbative effects are identified as a kind of instanton effects [2]∼ [7]. Moreover, we can explicitly formulate the T-duality in the noncritical string theory, for example, in the c = 1/2 string theory as discussed in [8].…”