Localization of effective actions in heterotic string field theory

Abstract

We consider the algebraic couplings in the tree level effective action of the heterotic string. We show how these couplings can be computed from closed string field theory. When the light fields we are interested in are charged under an underlying N = 2 R-charge in the left-moving sector, their quartic effective potential localizes at the boundary of the worldsheet moduli space, in complete analogy to the previously studied open string case. In particular we are able to compute the quartic closed string field theory potential without resorting to any explicit expression for the 3-and the 4-strings vertices but only using the L ∞ relations between them. As a non trivial example we show how the heterotic Yang-Mills quartic potential arises in this way.1

Classical algebraic structures in string theory effective actions

“…The resulting effective action is expressed via off-shell amplitudes for the gauge field where in addition to the usual worldsheet propagator b 0 L 0 (1 − P 0 ) there is also an "algebraic" propagator of the form 1 2 c 0 b −1 b 1 P 0 . This propagator (which already appeared in [8] in heterotic string field theory, with the understood superstring corrections) has been recently discussed by Sen in the context of string perturbation theory in D-instantons background [56] and our analysis offers a complementary (and equivalent in our tree-level treatment) viewpoint.…”

“…5 At this point it is important to remember that we have only established that it is consistent to fix Siegel gauge for the massive modes which are projected away by P0 (and which were already integrated out). It does not seem to be possible to fix Siegel gauge also for the modes ψ ∈ ker L0 in such a way that the corresponding out-of-Siegel equations would be trivialized by the in-Siegel equations of motion, as it was the case above for the massive modes [8]. 6 We thank the referee of this paper for pointing this out to us.…”

“…It is therefore manifest (see e.g. [8,15,62] and the references therein) that eom k should be interpreted precisely as the obstructions to exactness of the marginal deformation Ψ(ψ(λ)) arising at order λ k . The individual terms of Ψ(ψ(λ)) (as given by (2.96)) then exactly agree with order-by-order expansion of classical solution of the full SFT equation of motion which corresponds to a marginal deformation of the original perturbative vacuum.…”

“…So we would like to get rid of B(k). In [8], where a similar problem was solved to the first few orders in Heterotic String Field Theory, it was observed that setting the analogue of the B field to zero by imposing Siegel gauge would leave out-of-Siegel gauge equations which would not be accounted for by the remaining equations of motion (as instead it happens by fixing Siegel gauge for the massive fields). Therefore to get rid of the unphysical field B(k) we have to integrate it out.…”

“…In recent years complete constructions of super string field theories have become available [1][2][3][4][5][6][7] and there has been interest in explicitly computing the effective action of a given microscopic string field theory, after integrating out the massive degrees of freedom [8][9][10][11], as originally done in [12]. The construction of effective actions from string field theory is instrumental for both giving a useful low-dimensional handle on the space of classical solutions [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32] as well as for a better grounded approach to superstring perturbation theory [33][34][35][36][37][38][39][40][41][42][43].…”