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## Non-Critical Pure Spinor Superstrings (2006)

Citations: | 15 - 3 self |

### Citations

428 |
String theory. Vol. 2: Superstring theory and beyond
- Polchinski
- 1998
(Show Context)
Citation Context ...lity and is specific to d + 2 = 6. At the next level there are the NS vectors. The zero momentum states are Jµ = e −φ±iHI . (6.4) We now turn to the Ramond sector. We use Polchinski’s notation (α, F) =-=[30]-=-, where α is the space-time fermion index and F is the worldsheet spinor index, and denote the R operators by R F . The zero momentum R states with F = 1 are R 1 +++ = e−φ/2+i(H+H1 +H 2 )/2−ix/Q , R 1... |

391 |
Tseytlin, “Type IIB superstring action
- Metsaev, A
- 1998
(Show Context)
Citation Context ...ight-moving sector. The symmetry SO(2) acts as the R-symmetry on the space. The OSp(2|4) left invariant 1-form is expanded in the basis of generators of the supergroup (following Metsaev and Tseytlin =-=[32]-=-) as LµP µ +LµνJ µν +LIJΛ IJ +L I α Qα I . The pure spinors action then consists of three terms Sps = SGS + Sκ + Sgh, where the first term is the κ–symmetric GS action [3] ∫ SGS = d 2 zηµνL µ ∫ L¯ ν +... |

309 | Super Poincare covariant quantization of the superstring - Berkovits - 2000 |

186 | Conformal invariance, supersymmetry and string theory,
- Friedan, Martinec, et al.
- 1986
(Show Context)
Citation Context ... ˜κ . (2.33) This can be verified to have still a vanishing central charge c = (10)x + (−12)pθ + (2)˜ φ˜κ = 0 . a– 13 – The pure spinors are reconstructed by the ordinary bosonization of a βγ-system =-=[16]-=- λ + = e ˜ φ+˜κ , w+ = ∂κe −˜ φ−˜κ , (2.34) whose OPE is w+(z)λ + (0) ∼ 1 . (2.35) z But the naive stress tensor one would expect for this βγ-system w+∂λ + = − 1 2 (∂ ˜ φ) 2 + 1 2 (∂˜κ)2 − 1 2 ∂2 ˜ φ ... |

183 |
Notes on Quantum Liouville Theory and Quantum
- Seiberg
- 1990
(Show Context)
Citation Context ...rt as V ∼ e βϕ = e Q 2 ϕ e −Eϕ ≡ gS(ϕ)e −Eϕ , (4.7) such that the corresponding wavefunction Ψ(E) ∼ e −Eϕ is localized in the weak coupling region gs(ϕ) → 0. These operators satisfy the Seiberg bound =-=[24]-=- Reβ ≤ Q , (4.8) 2 There are also operators with complex β = Q/2 + ikϕ whose imaginary part is the momentum of the wavefunction of a particle moving in the ϕ direction. They correspond to propagating ... |

114 |
Multiloop amplitudes and vanishing theorems using the pure spinor formalism for the superstring,
- Berkovits
- 2004
(Show Context)
Citation Context ... Also we see that we need three ghost number one vertex operators for a nonvanishing tree level amplitude. Consider next a definition analgous to the pure spinor measure for the critical superstrings =-=[31]-=-. Let us recall first the critical case. The ghost number anomaly reads Jgh(z)T(0) ∼ Qgh + . . ., z3 with Q = −8. The generic pure spinor measure is d11λ as the pure spinor space is eleven-dimensional... |

99 |
ICTP lectures on covariant quantization of the superstring,” [arXiv:hepth/0209059
- Berkovits
(Show Context)
Citation Context ...y we came accross. 2. The pure spinor formalism In this section we will briefly review the main ingredients of the pure spinor formalism for critical superstrings in flat ten-dimensional target space =-=[5, 9]-=-. These structures will appear with some modifications in the pure spinor non-critical superstrings. We will consider for simplicity the open superstring. The generalization to the closed string case ... |

95 | The wall of the cave,”
- Polyakov
- 1999
(Show Context)
Citation Context ...erstring compactifications. Second, the study of non-critical superstrings in the context of the gauge/string correspondence may provide dual descriptions of new gauge theories, and in particular QCD =-=[2, 3]-=-. A complication in the study of non-critical superstrings in curved spaces is that, unlike the critical case, there is no consistent approximation where supergravity provides a valid effective descri... |

89 |
Two-dimensional models with (0,2) supersymmetry: Perturbative aspects, Adv.Theor.Math.Phys
- Witten
- 2007
(Show Context)
Citation Context ...α , wα) on different patches of the pure spinor space, which are compatible with their OPE. They are reflected by quantum anomalies in the worldsheet and pure spinor space holomorphic diffeomorphisms =-=[7]-=-. The critical superstring pure spinor space has a singularity at λ α = 0. Blowing up the singularity results in an anomalous theory. However, simply removing the origin leaves a nonanomalous theory [... |

86 |
Quantum consistency of the superstring
- Berkovits
(Show Context)
Citation Context ...n under the BRST symmetry can provide strong constraints on possible quantum correction. This has been used, for instance, to prove that AdS5 × S 5 is a consistent background for type II superstrings =-=[6]-=-. In this paper we will use a pure spinor formalism to describe non-critical superstrings. The strategy of constructing the pure spinor description of the non-critical superstrings is to first map the... |

86 | Ten-dimensional supergravity constraints from the pure spinor formalism for the superstring
- Berkovits, Howe
(Show Context)
Citation Context ...x operator has the expansion [13] U (1) = ∂λ α Aα + λ α ∂θ β Bαβ + ... . (2.22) In curved spaces the superspace field equations are derived by the requirement that λ α dα is holomorphic and nilpotent =-=[14]-=-. The construction of the closed superstrings is straightforward. One introduces the right moving superspace variables (¯pˆα, ¯ θ ˆα ), the pure spinor system ( ¯wˆα, ¯ λ ˆα ) and the nilpotent BRST o... |

61 |
Massive superstring vertex operator
- Berkovits, Chandia
- 2002
(Show Context)
Citation Context ...al and bosonic field strength, respectively. The analysis of the massive states proceeds in a similar way. At the first massive level the ghost number one weight one vertex operator has the expansion =-=[13]-=- U (1) = ∂λ α Aα + λ α ∂θ β Bαβ + ... . (2.22) In curved spaces the superspace field equations are derived by the requirement that λ α dα is holomorphic and nilpotent [14]. The construction of the clo... |

54 |
The Superembedding origin of the Berkovits pure spinor covariant quantization of superstrings, Nucl.Phys. B639
- Matone, Mazzucato, et al.
- 2002
(Show Context)
Citation Context ...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 ... |

54 |
Nieuwenhuizen, Covariant quantization of superstrings without pure spinor constraints
- Grassi, Policastro, et al.
(Show Context)
Citation Context ...eight zero is not empty: it contains several operators constructed as explained in (4.49). It would be interesting to explore this further. Another issue is the removal of the pure spinor constraints =-=[34]-=-. It has been shown in in [35] that removing the pure spinor constraint might lead to an infinite tower of ghost-for-ghosts, and it seems that, except a finite number of them, the rest of the ghost-fo... |

52 | Lectures on curved beta-gamma systems, pure spinors, and anomalies - Nekrasov |

52 | Holography for non-critical superstrings
- Giveon, Kutasov, et al.
- 1999
(Show Context)
Citation Context ...tates. We collect the various spectra in the following table: d = 0 d = 2 d = 4 gauge: 2 ⊕ 2 4 ⊕ 4 8 ⊕ 8 supergravity: − 8 ⊕ 8 32 ⊕ 32 (3.10) Consider the holographic interpretation in the d = 4 case =-=[20]-=-. The Liouville direction ϕ is the holographic direction. At the weak coupling end of the space ϕ = −∞ a four dimensional non-gravitational theory lives, which is non local and is called Little String... |

48 | Conformal fixed points of unidentified gauge theories,” Mod
- Polyakov
(Show Context)
Citation Context ...erstring compactifications. Second, the study of non-critical superstrings in the context of the gauge/string correspondence may provide dual descriptions of new gauge theories, and in particular QCD =-=[2, 3]-=-. A complication in the study of non-critical superstrings in curved spaces is that, unlike the critical case, there is no consistent approximation where supergravity provides a valid effective descri... |

41 |
Relating the RNS and pure spinor formalisms for the superstring, JHEP 0108
- Berkovits
- 2001
(Show Context)
Citation Context ...the map will contain the contribution of the holomorphic top form on the pure spinor space. Indeed this term is necessary for a consistent definition of the pure spinor βγ-system [8, 7]. Note that in =-=[15]-=- a similar map from the RNS variables to the pure spinor ones has been constructed, but with no consideration of the βγ-system structure and the holomorphic top form. In the following we will consider... |

37 | Classical superstring mechanics, Nucl. Phys - Siegel - 1985 |

33 | Notes on noncritical superstrings in various dimensions
- Murthy
(Show Context)
Citation Context ...try algebra in the various dimensions and show explicitely its current algebra case by case. 3.2 Spectrum In this section, we will collect some useful results about the spectrum in various dimensions =-=[19]-=-, that we will compare to the pure spinor covariant cohomology computation. Consider first various general features of the superstring, which are valid in all non-critical dimensions on the background... |

29 | The character of pure spinors,
- Berkovits, Nekrasov
- 2005
(Show Context)
Citation Context ...ntains several operators constructed as explained in (4.49). It would be interesting to explore this further. Another issue is the removal of the pure spinor constraints [34]. It has been shown in in =-=[35]-=- that removing the pure spinor constraint might lead to an infinite tower of ghost-for-ghosts, and it seems that, except a finite number of them, the rest of the ghost-for-ghosts are the same in all d... |

22 |
A new description of the superstring
- Berkovits
(Show Context)
Citation Context ...ymmetric radius we already know from RNS analysis. Note that the hermiticity property of the action and the stress tensor implies that the hermiticity properties of the variables is not the naive one =-=[25]-=-. 4.3.1 Supersymmetry structure An important ingredient in the construction of the pure spinor non-critical superstring is the supersymmetry algebra and the superspace structure. Let us construct the ... |

21 | Observations on the moduli space of two dimensional string theory,” JHEP 03
- Seiberg
- 2005
(Show Context)
Citation Context ...ralize the non-critical pure spinor action to other backgrounds with a larger amount of supersymmetries. We first recall some facts about the RNS computation of the spectrum and supersymmetry algebra =-=[21, 22, 23]-=-. Then we will introduce the map to the pure spinor variables and reconstruct the full covariant theory. We will compute the cohomology and show that it agrees to the RNS spectrum. Eventually, we will... |

20 | BRST Cohomology and Physical States in 2D Supergravity Coupled to ĉ ≤ 1
- Itoh, Ohta
- 1992
(Show Context)
Citation Context ...ralize the non-critical pure spinor action to other backgrounds with a larger amount of supersymmetries. We first recall some facts about the RNS computation of the spectrum and supersymmetry algebra =-=[21, 22, 23]-=-. Then we will introduce the map to the pure spinor variables and reconstruct the full covariant theory. We will compute the cohomology and show that it agrees to the RNS spectrum. Eventually, we will... |

15 |
BFT embedding of the Green-Schwarz superstring and the pure spinor formalism,”
- Gaona, Garcia
- 2005
(Show Context)
Citation Context ...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 ... |

14 |
Ground ring for the 2-D
- Bouwknegt, McCarthy, et al.
- 1992
(Show Context)
Citation Context ...portance of the similarity transformation. In the two-dimensional superstrings, there is a special set of operators in the BRST cohomology at spin zero and ghost number zero, known as the ground ring =-=[33, 23]-=-. In the pure spinor formulation of two-dimensional type II non-critical string, as discussed in section 4, the cohomology at ghost number zero and weight zero is not empty: it contains several operat... |

13 |
Lower-dimensional pure-spinor superstrings
- Grassi, Wyllard
(Show Context)
Citation Context ...rfield. If we choose Ω = −M, we are left with AI1 = DI1N, AI2 = −DI2N , (5.41) for a generic superfield N. It is easy to see that the degrees of freedom encoded in V are 4 ⊕ 4, which is the result of =-=[29, 26]-=-. 14 Since we are interested in the SO(1, 1) supersymmetry multiplet, we have to eliminate the θ ˙+i components in the vertex operator, keeping only the θ +i , the latter entering in the holomorphic s... |

12 |
Non-supersymmetric deformations of non-critical superstrings
- Itzhaki, Kutasov, et al.
- 1977
(Show Context)
Citation Context ...radius. 2 In other words, the radius changing operator is not an N = 2 primary. For 2 The stability of the linear dilaton background away from the supersymmetric radius has been recently discussed in =-=[18]-=-.– 16 – the (2n+2)-dimensional superstrings we can construct 2 n+2 candidates for space-time supercurrents in the − 1 2 picture q ∼ e φ i − + 2 2(±H±H 1 ±...±Hn±Qx) , (3.7) with the usual bosonizatio... |

12 |
On the Berkovits covariant quantization
- Oda, Tonin
(Show Context)
Citation Context ...egrees of freedom as before, but with different space-time charges. The interesting observation is that the BRST charge Q = QB+Q ′ can be derived by a GS-like action through the usual Oda–Tonin trick =-=[37]-=-. Consider now the four dimensional pure spinor action in the linear dilaton background (5.22). It is invariant with respect to the pure spinor operator (F.1) but not with respect to the total BRST op... |

11 |
Some properties of (non)critical strings
- Kutasov
(Show Context)
Citation Context ...2.11). This will be discussed in a separate work. 3. RNS non-critical superstrings In this section we will consider the RNS description of superstrings propagating in the d + 2 dimensional background =-=[1, 17]-=- with flat metric in the string frame and a linear dilaton R 1,d−1 × Rϕ × U(1)x , (3.1) Φ = Q ϕ . 2 The effective string coupling gs = e Φ varies as we move along the ϕ direction and when considering ... |

11 |
Pure-spinor superstrings in d
- Wyllard
- 2005
(Show Context)
Citation Context ... d = 0 case we discussed in (4.39), by looking at the mode expansion of the pure spinor constraint (5.34) or alternatively by analyzing the OPE’s involving the Lorentz generator and the ghost current =-=[26, 28]-=-. Let us compute the cohomology now. As discussed in the two-dimensional case, there are two different kinds of vertex operators at ghost number one and weight zero. The first one is V (1) = λ Ii AIi(... |

9 |
Origin of pure spinor superstring, JHEP 05
- Aisaka, Kazama
- 2005
(Show Context)
Citation Context ...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 ... |

8 |
Morales Morera, “Partition functions of pure spinors
- Grassi, F
(Show Context)
Citation Context ...+ = 0, ∂λ + λ ˙+ − λ + ∂λ ˙+ = 0. (4.38) The first condition is the pure spinor constraint itself. The derivative condition is a consequence of the first condition. There are various ways to see this =-=[26]-=-. The simplest is to expand the condition λ + λ ˙+ = 0 in modes λ + 0 λ ˙+ 0 = 0, λ + 0 λ ˙+ 1 + λ + 1 λ ˙+ 0 = 0, . . . (4.39) Then for a solution of the zero mode λ + 0 ̸= 0, the second equation imp... |

5 |
Non-critical covariant superstrings
- Grassi, Oz
(Show Context)
Citation Context ...nteresting target space curved geometries include RR field fluxes. As in the critical superstrings case, the RNS formulation is inadequate for the quantization of superstrings in such backgrounds. In =-=[4]-=- a covariant description of non-critical superstrings in even dimensions has been constructed using the hybrid type variables. The approach taken was to construct a covariant description of non-critic... |