The GSO projection, BRST cohomology and picture-changing in N = 2 string theory (original) (raw)
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From N=2 Fermionic Strings to Superstrings?
I review the covariant quantization of the critical N=2 fermionic string with and without a global Z 2 twist. The BRST analysis yields massless bosonic and fermionic vertex operators in various ghost and picture number sectors, as well as picture-changers and their inverses, depending on the field basis chosen for bosonization. Two distinct GSO projections exist, one (untwisted) retaining merely the known bosonic scalar and its spectral-flow partner, the other (twisted) yielding two fermions and one boson, on the massless level. The absence of interactions in the latter case rules out standard spacetime supersymmetry. In the untwisted theory, the U(1, 1)-invariant three-point and vanishing four-point functions are confirmed at tree level. I comment on the N=2 string field theory, the integration over moduli and the realization of spectral flow.
On the BRST operator structure of the N = 2 string
Nuclear Physics B, 1993
The BRST operator cohomology of N = 2 2d supergravity coupled to matter is presented. Descent equations for primary superfields of the matter sector are derived. We find one copy of the cohomology at ghost number one, two independent copies at ghost number two, and conjecture that there is a copy at ghost number three. The N = 2 string has a twisted N = 4 superconformal symmetry generated by the N = 2 superstress tensor, the BRST supercurrent, the antighost superfield, and the ghost number supercurrent.
Chiral BRST Cohomology of N = 2 Strings at Arbitrary Ghost and Picture Number
Communications in Mathematical Physics, 1999
We compute the BRST cohomology of the holomorphic part of the N =2 string at arbitrary ghost and picture number. We confirm the expectation that the relative cohomology at non-zero momentum consists of a single massless state in each picture. The absolute cohomology is obtained by an independent method based on homological algebra. For vanishing momentum, the relative and absolute cohomologies both display a picture dependence -a phenomenon discovered recently also in the relative Ramond sector of N =1 strings by Berkovits and Zwiebach [1]. * supported in part by the 'Deutsche Forschungsgemeinschaft'; grant LE-838/5-1
18 2 v 1 2 0 M ay 2 00 3 1 Superstring Field Theory Action Including Massless Fermions
2003
During the 80’s a string field theory was developed for the open bosonic string theory, following the ideas of witten for the role of noncommutativity in the string theory product (witten’s midpoint interaction) and the development of BRST techniques in string theory [1]. The natural generalization of these ideas to the case of the superstring theory didn’t achieved the success of the bosonic theory due to the divergences at the tree level for the classical action, a consequence of picture changing operators appearing explicitly in the action [2]. The interest on this kind of theories declined substantially, mainly because of the lack of any significant progress, till Sen’s conjecture on the role of tachyon in a system of unstable D-branes [3], arguing that the tachyon should have a minimum for its potential at the point where the system undergoes a decay, establishing a value for the minimum of the tachyon potential as the value of the tension of the original unstable D-brane syste...
Physical Review D, 1995
The most general homogeneous monodromy conditions in N=2 string theory are classified in terms of the conjugacy classes of the global symmetry group U(1, 1) ⊗ Z 2 . For classes which generate a discrete subgroup Γ, the corresponding target space backgrounds C 1,1 /Γ include half spaces, complex orbifolds and tori. We propose a generalization of the intercept formula to matrix-valued twists, but find massless physical states only for Γ=1 (untwisted) and Γ=Z 2 (à la Mathur and Mukhi), as well as for Γ being a parabolic element of U(1, 1). In particular, the sixteen Z 2 -twisted sectors of the N=2 string are investigated, and the corresponding ground states are identified via bosonization and BRST cohomology. We find enough room for an extended multiplet of 'spacetime' supersymmetry, with the number of supersymmetries being dependent on global 'spacetime' topology. However, world-sheet locality for the chiral vertex operators does not permit interactions among all massless 'spacetime' fermions.
More about picture-changed vertices in superstring theory
Physics Letters B, 1991
We construct explicitly the lowest picture-changed vertex operators in superstring theory. We show, in particular, that the terms with (b, c) ghost number q= 1 are of the form c(z) V(z) as the vertex operators in the hosonic string case. 1. In superstring theory the space-time quantum numbers of a physical state are carried by a super vertex operator that we will denote by V(z, O) = Vo(z) +OV, (z). (1) The integral of (1) over superspace is required to be conformal invariant; therefore it must be a superconformal field with conformal weight 3 = ½. The two components of the super-vertex operator corresponding, for instance, to the tachyon and photon states are given by V~o(Z)=:eik "(:~: , VS=:e'lp'(z) eikx~z): , V](z)=:ik.q/(z) eihx(-~:, VP(z)=:[e'~x(z)+ik'~u(z)e'~/(z)]eikx(z~:, (2) with k2~-1 for the tachyon and with e.k= 0 and k2= 0 for the photon. In a BRST invariant formalism the reparametrization ghosts (b, c) and the superconformal ones (//, y) must be properly included in the definition of the vertex operators. It turns out that for each physical state one can associate an infinite set of vertex operators corresponding to different values of the total ghost number q + q', q and q' being the eigenvalues of the U (1) ghost number currents associated respectively to the (b, c) and (/~, 7) systems. Indeed it is possible to transform BRST invariant vertex operators to new ones carrying the same space-time quantum numbers but a different eigenvalue of the total ghost number. This transformation is performed by the picture-changing operation [ 1 ].
Spacetime supersymmetry of extended fermionic strings in 2+2 dimensions
Classical and Quantum Gravity, 1993
The N = 2 fermionic string theory is revisited in light of its recently proposed equivalence to the non-compact N = 4 fermionic string model. The issues of spacetime Lorentz covariance and supersymmetry for the BRST quantized N = 2 strings living in uncompactified 2+2 dimensions are discussed. The equivalent local quantum supersymmetric field theory appears to be the most transparent way to represent the space-time symmetries of the extended fermionic strings and their interactions. Our considerations support the Siegel's ideas about the presence of SO(2, 2) Lorentz symmetry as well as at least one self-dual space-time supersymmetry in the theory of the N = 2(4) fermionic strings, though we do not have a compelling reason to argue about the necessity of the maximal space-time supersymmetry. The world-sheet arguments about the absence of all string massive modes in the physical spectrum, and the vanishing of all string-loop amplitudes in the Polyakov approach, are given on the basis of general consistency of the theory.
A heterotic N=2 string with space–time supersymmetry
Nuclear Physics B, 2001
We reconsider the issue of embedding space-time fermions into the four-dimensional N =2 world-sheet supersymmetric string. A new heterotic theory is constructed, taking the right-movers from the N =4 topological extension of the conventional N =2 string but a c=0 conformal field theory supporting target-space supersymmetry for the left-moving sector. The global bosonic symmetry of the full formalism proves to be U (1, 1), just as in the usual N =2 string. Quantization reveals a spectrum of only two physical states, one boson and one fermion, which fall in a multiplet of (1, 0) supersymmetry.