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...ich is twice the complex dimension of the pure spinor space T(w,λ)(z)T(w,λ)(0) ∼ dimC(M) z 4 + ... . (2.9) 1 There have been various attempts to derive the pure spinor formalism from first principles =-=[10, 11, 12]-=-.– 9 – The ghost number anomaly reads J(w,λ)(z)T(w,λ)(0) ∼ − 8 c1(Q) + ... = + ... , (2.10) z3 z3 where c1(Q) is the first Chern class of the pure spinor cone base Q. The physical states are defined ...

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...us how it can be obtained by gauge fixing a reparametrisation invariant worldsheet action. On the other hand there exist some proposals to find more geometrical version of the pure spinor formalism 1=-=[14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 8]-=- and for recent discussion of these approaches we recommend the paper [31] where new promising formulation of the pure spinor formalism was also proposed. In summary, the super-Poincare covariant form...

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...Wrapped [95] or Galilean [96] M2-brane theory. A membrane action for this theory was constructed in [101]. In the exploration of noncommutativity in string/M theory, boundary conditions play a central role. Following ideas in [102], the work [103] gave a prescription for treating boundary conditions as second-class constraints in a manner that is fully compatible with Dirac’s method. Another important development that has taken place in the past few years is the work of Berkovits on the quantization of the superstring in a manifestly super-Poincaré- covariant way (for a review, see [104]). In [105] a connection between this new ‘pure spinor’ method and the standard Green-Schwarz formalism was established by working out for the latter the Batalin-Fradkin-Tyutin program for converting second-class constraints into first-class ones (see also [106]). On the more mathematical side, it is well known that twistor methods are suitable to describe Yang-Mills instantons which receive corrections from string theory in powers of α ′. The description of full-fledged Yang-Mills fields can be also addressed through twistor methods, which is known as the Witten-Isenberg-Yasskin-Green (WIYG) corresponde...

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...lated works, see [13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23]. 3 The problem how pure spinor formalism arises from the conventional GS formalism was attached in many papers from several point of view =-=[24, 25, 26, 28, 29, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39]-=-. – 1 –starting point is the pure spinor action in general background that was introduced in [41] 4 . As opposite to the original work [41] we formulate the pure spinor action with general worldsheet...

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...e transformations (2.5) involving (wµ, ˆwµ) suggests that this symmetry should be gauge fixed at the quantum level in some way. There are many proposals as how to deal with the pure spinor constraint =-=[25, 26, 27, 28, 29, 30]-=- with no definite widely accepted conclusion. 4 We work in units 2πα ′ = 1. 33. Hamiltonian analysis In this section we are going to perform the Hamiltonian analysis of the action (2.1). Our analysis...

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... the superstring [1]. This formalism has passed many tests since it was formulated. It describes correctly the superstring spectrum in the light cone gauge [2], in semi light cone gauge [3] (see also =-=[4]-=-) and in a manifestly ten dimensional covariant manner [5]. It has also been possible to compute amplitudes by using this formalism. Tree-level amplitudes were shown to coincide with the RNS result in...

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...at the pure-spinor formulation can be obtained from the superembedding formalism. In addition, in the modified GS action given in [22], one can see the pure-spinor BRST operator emerging. Finally, in =-=[23]-=- the BFT embedding is used to motivate the BRST operator. 13Another interesting question to understand is how the Virasoro constraints are implemented in the new framework. Let us elaborate on this i...