#### DMCA

## One-loop Superstring Amplitude From Integrals on

Venue: | Pure Spinors Space,” JHEP 0912 (2009) 034. [arXiv:0910.3405 [hep-th |

Citations: | 13 - 3 self |

### Citations

1338 |
Representation Theory
- Fulton, Harris
- 1991
(Show Context)
Citation Context ...ngs to the H20(CP 15) = Z homology group [34], so the projective pure spinors space is proportional to the [ CP 10 ] homology class because CP 10 is the generator of the H20(CP 15) homology group [34]=-=[32]-=-. The proportionality factor is called the “ degree” of a variety and it is a integer number since H20(CP 15) = Z. The degree of projective pure spinors is given by degree(SO(10)/U(5)) = #(SO(10)/U(5)... |

309 |
Super Poincare covariant quantization of the superstring
- Berkovits
- 2000
(Show Context)
Citation Context ...ction The pure spinor formalism has many advantages for computing scattering amplitudes compared to the RNS and the GS formalism. For example, it does not have to deal with worldsheet spin structures =-=[2]-=-[25], it has manifest Super-Poincaré invariance and incorporate in a natural way the Ramond sectors. Nevertheless the formalism presents some difficulties, for example, the normalization of the integ... |

203 |
A basic course in algebraic topology
- Massey
- 1991
(Show Context)
Citation Context ...five holomorphic homogeneous polynomials [33][2] 2λ+λa − 1 4 ǫabcdeλbcλde = 0, a = 1, ..., 5. (4.16) As SO(10)/U(5) is a closed manifold on CP 15, then it belongs to the H20(CP 15) = Z homology group =-=[34]-=-, so the projective pure spinors space is proportional to the [ CP 10 ] homology class because CP 10 is the generator of the H20(CP 15) homology group [34][32]. The proportionality factor is called th... |

141 |
The theory of spinors
- Cartan
- 1967
(Show Context)
Citation Context ...] 2λ+λa − 1 4 ǫabcdeλbcλde = 0, a, b, c, d, e = 1, 2, ..., 5 (2.9) 2λbλab = 0. (2.10) where just five equations are linearly independent. In the chart U+++++ = {λ+ 6= 0} these equations are solved by =-=[33]-=- λ+ = γ, λab = γuab, λ a = 1 8 γǫabcdeubcude. (2.11) As the uab variables parametrize the projective pure spinors space, then it is clear that the pure spinors space is the total space of the O(−1) bu... |

114 |
Multiloop amplitudes and vanishing theorems using the pure spinor formalism for the superstring,
- Berkovits
- 2004
(Show Context)
Citation Context ...cd(w)→ δc[aδdb](z − w)−1. (2.16) For the sα, rα fields the procedure is similar. From the previous definitions of the space-time dimensions of the fields and their OPEs we can get the following OPE’s =-=[23]-=- dα = pα − 1 α′ γmαβθ β∂xm − 1 4α′ γmαβγmγδθ βθγ∂θδ, Πm = ∂xm + 1 2 θγm∂θ, dα(z)dβ(w) ∼ − 2 α′ γmαβΠm z − w , dα(z)Π m(w) ∼ γ m αβ∂θ β z − w , dα(z)f(θ(w), x(w)) ∼ (z −w)−1Dαf(θ(w), x(w)), where Dα = ... |

106 |
The Geometry Of String Perturbation Theory
- D’Hoker, Phong
- 1988
(Show Context)
Citation Context ...on The pure spinor formalism has many advantages for computing scattering amplitudes compared to the RNS and the GS formalism. For example, it does not have to deal with worldsheet spin structures [2]=-=[25]-=-, it has manifest Super-Poincaré invariance and incorporate in a natural way the Ramond sectors. Nevertheless the formalism presents some difficulties, for example, the normalization of the integrati... |

96 | Superstring Modifications Of Einstein’s Equations - Gross, Witten - 1986 |

65 |
Evaluation Of The One Loop String Path
- Polchinski
- 1986
(Show Context)
Citation Context ...ation constant of the massless vertex operator. Its precise value will not be needed here. The 1/2 factor is needed because the total group of automorphism on the torus is SL(2,Z) instead of PSL(2,Z) =-=[26]-=-[27]. As the amplitude is computed using the bosonic string prescription, we must 6 take in account the normalization of the inner product between the b-ghost and the Beltrami differential in the same... |

64 | Two loops in eleven dimensions”, Phys - Green, Kwon, et al. - 2000 |

61 |
Pure spinor formalism as an
- Berkovits
- 2005
(Show Context)
Citation Context ...o normalize the massless vertex operator in the same way as in the D’Hoker, Phong and Gutperle’s paper [14]. The superstring theory action in the right sector of the non-minimal pure spinor formalism =-=[3]-=- is given by S = 1 2πα′ ∫ Σg d2z ( ∂xm∂̄xm + α ′pα∂̄θ α − α′ωα∂̄λα − α′ω̄α∂̄λ̄α + α′sα∂̄rα ) (2.1) where we define the space time dimensions of the variables and coupling constant α′ as follows [xm] =... |

52 | Lectures on curved beta-gamma systems, pure spinors, and anomalies
- Nekrasov
(Show Context)
Citation Context ...etrize the projective pure spinors space, then it is clear that the pure spinors space is the total space of the O(−1) bundle over the projective pure spinors space with blow-up at the origin (γ = 0) =-=[11]-=- [7] [10]. In this chart, we can take the gauge ωa = ω̄ a = 0 and the parametrization ω+ = β − 1 2γ vabuab, ω ab = vab γ , (2.12) ω̄+ = β̄ − 1 2γ̄ v̄abū ab, ω̄ab = v̄ab γ̄ , (2.13) so the pure spinor... |

52 | Multiloop superstring amplitudes from non-minimal pure spinor formalism,
- Berkovits, Nekrasov
- 2006
(Show Context)
Citation Context ...z (pα + 1 α′ γmαβθ β∂xm + 1 12α′ γmαβγmγδθ βθγ∂θδ) and it satisfies the algebra {qα, qβ} = 2 α′ γmαβ ∫ dz ∂xm, [qα,Π m(z)] = 0, {qα, dβ(z)} = 0. (2.17) The construction of the b-ghost is such that [3]=-=[29]-=- {Q, b(z)} = T (z), where Q = ∫ dz (λαdα + ω̄ αrα), T (z) = − 1 α′ ∂xm∂xm − pα∂θα + ωα∂λα + ω̄α∂λ̄α − sα∂rα. Since Q and T are space time dimensionless so is b, which is given by b = sα∂λ̄α + λ̄α(2Π m... |

45 |
String Theory Vol 1
- Polchinski
- 1998
(Show Context)
Citation Context ...zation of the previous Section we will compute the one loop amplitude for 4-massless vertex operator in the NS-NS sector. Although the general structure of this Section can be found in the references =-=[27]-=-[23][16][22], we include it to justify the normalization of the measures and to find the overall constant factor for the amplitude, which has not been computed. As non-minimal pure spinor formalism is... |

44 | Equivalence of two-loop superstring amplitudes in the pure spinor and RNS formalisms”, hep-th/0509234; C. Mafra, “Four-point one-loop amplitude computation in the pure spinor formalism - Berkovits, Mafra |

37 |
Some Superstring Amplitude Computations with the Non-Minimal Pure Spinor Formalism
- Berkovits, Mafra
- 2006
(Show Context)
Citation Context ... the path integral measures. In the Subsection 3.2 we compute the contribution of the others fields and discuss biefly the modular invariance of the scattering amplitude. We use some results found in =-=[4]-=-[21][16][22] in which the authors showed: 1) the equivalence between the kinematic factor of the non-minimal pure spinor formalism and the minimal pure spinors formalism, 2) the equivalence between th... |

36 |
Constraints And Field Equations For Ten-Dimensional Superyang-Mills Theory,” Commun
- Harnad, Shnider
- 1986
(Show Context)
Citation Context ...dγmnpd+ 24NmnΠp) 192(λλ̄)2 − α′ 2 (rγmnpr)(λ̄γ md)Nnp 16(λλ̄)3 + α′ 2 (rγmnpr)(λ̄γ pqrr)NmnNqr 128(λλ̄)4 . 5 In order to build the vertex operators we use the following N = 1 SYM θ expansions [22][23]=-=[24]-=- Aα(x, θ) = 1 2 am(γ mθ)α − 1 3 (ξγmθ)(γ mθ)α − 1 32 Fmn(γpθ)α(θγ mnpθ) + ... (2.18) Am(x, θ) = am − (ξγmθ)− 1 8 (θγmγ pqθ)Fpq + 1 12 (θγmγ pqθ)(∂pξγqθ) + ... (2.19) Wα(x, θ) = ξα − 1 4 (γmnθ)αFmn + 1... |

29 | The character of pure spinors,
- Berkovits, Nekrasov
- 2005
(Show Context)
Citation Context ...he Kähler form of the pure spinors space in any dimension is given by ΩD=2n = 1 (λλ̄) dimCPS−c1 dimCPS ∂∂̄(λλ̄), (4.5) where c1 = 2n−2 is the first Chern class of the tangent bundle over SO(2n)/U(n) =-=[5]-=- and dimCPS = n(n−1)2 +1 is the complex dimension of the pure spinors space. Writing (4.2) in the coordinates (2.11) we get∫ [dλ][dλ̄] e−aλλ̄ = ∫ (γγ̄)7dγ ∧ dγ̄ ∧ a<b, c<d duabdū cd e−aγγ̄(1+ 1 2 uab... |

27 |
Four-point one-loop amplitude computation in the pure spinor formalism
- Mafra
- 2006
(Show Context)
Citation Context ...th integral measures. In the Subsection 3.2 we compute the contribution of the others fields and discuss biefly the modular invariance of the scattering amplitude. We use some results found in [4][21]=-=[16]-=-[22] in which the authors showed: 1) the equivalence between the kinematic factor of the non-minimal pure spinor formalism and the minimal pure spinors formalism, 2) the equivalence between the kinema... |

27 | Superstring scattering amplitudes with the pure spinor formalism”, arXiv:0902.1552 [hep-th
- Mafra
(Show Context)
Citation Context ...ntegral measures. In the Subsection 3.2 we compute the contribution of the others fields and discuss biefly the modular invariance of the scattering amplitude. We use some results found in [4][21][16]=-=[22]-=- in which the authors showed: 1) the equivalence between the kinematic factor of the non-minimal pure spinor formalism and the minimal pure spinors formalism, 2) the equivalence between the kinematic ... |

24 | Pure Spinor Superspace Identities for Massless Four-point Kinematic Factors
- Mafra
(Show Context)
Citation Context ...s, called C2, in the non-minimal pure spinor formalism [31] and to show that the S-duality constraint (C21 = 2π 2C0C2)[14] is a consequence of the identities for massless four-point kinematic factors =-=[20]-=-. 2 Review on the non-minimal pure spinor formalism We will give a brief review of the non-minimal pure spinor formalism. The idea is to introduce our own conventions and to normalize the massless ver... |

21 | Two-loop superstrings and S-duality
- D’Hoker, Gutperle, et al.
(Show Context)
Citation Context ... - Universidade Estadual Paulista Caixa Postal 70532-2 01156-970 São Paulo, SP, Brazil Abstract In the Type II superstring the 4-point function for massless NS-NS bosons at one-loop is well known [1]=-=[14]-=-. The overall constant factor in this amplitude is very important because it needs to satisfy the unitarity and S-duality conditions [14]. This coefficient has not been computed in the pure spinor for... |

15 | The one-loop open superstring massless five-point amplitude with the non-minimal pure spinor formalism
- Mafra, Stahn
(Show Context)
Citation Context ...e path integral measures. In the Subsection 3.2 we compute the contribution of the others fields and discuss biefly the modular invariance of the scattering amplitude. We use some results found in [4]=-=[21]-=-[16][22] in which the authors showed: 1) the equivalence between the kinematic factor of the non-minimal pure spinor formalism and the minimal pure spinors formalism, 2) the equivalence between the ki... |

12 | Pure spinors are higher-dimensional twistors - Berkovits, Cherkis |

12 |
private communication
- Berkovits
(Show Context)
Citation Context ...is in perfect agreement with the result found by D’hoker, Phong and Gutperle in [14] up to a (α′/2)8 factor. Is easy to see that this factor is needed in order to have the right space-time dimensions =-=[30]-=-. Hence the amplitude found in [14] by D’hoker, Phong and Gutperle missed this term. Acknowledgments I am grateful to Carlos Mafra for useful conversations, correspondences and references. I especiall... |

10 |
One Loop Amplitudes And Effective Action
- Sakai, Tanii
- 1987
(Show Context)
Citation Context ...ESP - Universidade Estadual Paulista Caixa Postal 70532-2 01156-970 São Paulo, SP, Brazil Abstract In the Type II superstring the 4-point function for massless NS-NS bosons at one-loop is well known =-=[1]-=-[14]. The overall constant factor in this amplitude is very important because it needs to satisfy the unitarity and S-duality conditions [14]. This coefficient has not been computed in the pure spinor... |

6 |
Hilbert space of curved βγ systems on quadric cones
- Aisaka, Arroyo
(Show Context)
Citation Context ...n the 20-form (4.10). 22 We can get the same result (A.13) from the partition function, for example, computing the partition function for O(−1) over CPn in the zero level with the reducibility method =-=[13]-=- we have ZO(−1)(t) = 1 (1− t)n+1 . (A.20) Expanding around to ǫ = 1− t = 0 the most singular term is 1 ǫn+1 , (A.21) and by comparing with the Riemann-Roch formula (4.21) we get (A.13). Now we discuss... |

5 | On first order formalism in string theory,” Phys - Losev, Marshakov, et al. - 2006 |

3 |
and Loring W.Tu “Differential Forms in Algebraic Topology”, [SpringerVerlag published
- Bott
- 1982
(Show Context)
Citation Context ...result was expected, since Q8 is a hypersurface given by a homogeneous polynomial of degree 2, then the first Chern class of the divisor [Q8] is c1([Q8]) = 2H, (A.31) which is Poincaré dual to Q8 [7]=-=[8]-=-. So∫ Q8 c1(L) 6 = ∫ Q8 (f∗H)6 = ∫ CP 7 H6 ∧ c1([Q8]) = 2 ∫ CP 7 H7 = 2. (A.32) where f : Q8 → CP 7 is the embeding. We now have a geometric interpretation to the result found in [5]. In [5] it was sh... |