# Significance of massive states in string theory

A free superstring has an infinite tower of states with increasing mass. The massless states correspond to the fields of the corresponding SUGRA. In "Quantum Fields and Strings: A Course for Mathematicians", vol. II p. 899 we find that the massive states do not contribute anything new to the possible string backgrounds. Terms in the string action corresponding to coupling to a massive background field are nonrenormalizable and therefore disappear when we RG-flow to the IR fixed point, which is the CFT we actually use in quantum string theory. Actually it is explained for the bosonic string but I don't think the difference is essential

What is the physical meaning of this result?

Does it mean massive string states are solitons of the massless fields? If so, do these solitons exist in classical SUGRA?

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Massive string modes have masses of order the string mass $M_s$, independent of the string coupling $g_{str}$, whereas solitons have masses of order $1/g_{str}$ or $1/g_{str}^2$, depending on whether they are open or closed string solitons. So that putative matching does not work (the exponential degeneracy of massive string states would be another obstacle).

I believe the statement you are referring to does not have the wide ranging implications you draw from it, it has to do specifically with mechanics of computing S-matrix elements via string perturbation theory. In such computations in the background of massless modes, the contribution of the massive strings is already accounted by the usual procedure of summing over Riemann surfaces. This is explained nicely by this classic paper by Dine and Seiberg, Microscopic Knowledge From Macroscopic Physics In String Theory.

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Thx, do you know whether this article can be obtained freely online? –  Squark Feb 4 '12 at 20:58
There is a link to a scanned document from KEK in the page I linked to. –  user566 Feb 4 '12 at 21:19
Great, thanks!! –  Squark Feb 5 '12 at 9:31
I looked at the article but I am still confused, probably due to my own stupidity. I find it hard to reconcile the following 3 statements (maybe one of them is wrong): –  Squark Feb 5 '12 at 12:04
1. The moduli space of (appropriate) CFTs is the space of solutions of the "classical string equations of motion" –  Squark Feb 5 '12 at 12:05

The interactions of a massive particle fall off exponentially with distance (massless particles have long-range interactions), the exponent determined by the mass. Mathematically, this dependence is governed by the quadratic term of the field in the action.

Now let's lump all fields together into a multi-index field. Then the vacuum state(s) corresponds to the minimum energy configuration(s), and the nearby shape of the landscape around that minimum (those minima) is determined by the massive fields. Adding more of these fields won't change the space of minima or the long-range behavior of interactions.

Or is that too nontechnical and hand-wavy?

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