Conformal invariance, supersymmetry and string theory

Friedan, Daniel; Martinec, Emil J.; Shenker, Stephen H.

doi:10.1016/0550-3213(86)90356-1

Cited by 1,517 publications

(1,585 citation statements)

References 104 publications

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“…Using (4.23) we immediately get (4.27) Using the decomposition (4.16) and introducing a new operator 28) this can be written as (4.29) Now in contrast to the origial Π µ , the operator P I has a first class OPE with itself due to the contraction with the null vector field N µ I . Indeed, we have 30) where the null nature of N µ I is crucial for the disappearance of the double pole and (4.31) Note that S IJ is properly antisymmetric again due to the null property of N µ I .…”

Section: New First Class Algebramentioning

confidence: 99%

A new first class algebra, homological perturbation and extension of pure spinor formalism for superstring

Aisaka

Kazama

2003

J. High Energy Phys.

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Based on a novel first class algebra, we develop an extension of the pure spinor (PS) formalism of Berkovits, in which the PS constraints are removed. By using the homological perturbation theory in an essential way, the BRST-like charge Q of the conventional PS formalism is promoted to a bona fide nilpotent chargeQ, the cohomology of which is equivalent to the constrained cohomology of Q. This construction requires only a minimum number (five) of additional fermionic ghost-antighost pairs and the vertex operators for the massless modes of open string are obtained in a systematic way. Furthermore, we present a simple composite "b-ghost" field B(z) which realizes the important relation T (z) = {Q, B(z)}, with T (z) the Virasoro operator, and apply it to facilitate the construction of the integrated vertex. The present formalism utilizes U(5) parametrization and the manifest Lorentz covariance is yet to be achieved. †

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Section: New First Class Algebramentioning

confidence: 99%

A new first class algebra, homological perturbation and extension of pure spinor formalism for superstring

Aisaka

Kazama

2003

J. High Energy Phys.

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“…As we shall discover in sections IV A -IV C this is indeed possible. The non-unitary c = −2 minimal model has received a great deal of attention in recent years as a theory of dense polymers [64,65], as a celebrated example of a logarithmic conformal field theory [62,[66][67][68][69][70], and as a conformal ghost system [71]. The structure of this theory is rather rich and is known to consist of several sectors.…”

Section: Dense Polymers and Twist Operatorsmentioning

confidence: 99%

Disordered Dirac fermions: the marriage of three different approaches

Bhaseen¹,

Caux²,

Kogan³

et al. 2001

Nuclear Physics B

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We compare the critical multipoint correlation functions for twodimensional (massless) Dirac fermions in the presence of a random su(N ) (non-Abelian) gauge potential, obtained by three different methods. We critically reexamine previous results obtained using the replica approach and in the limit of infinite disorder strength and compare them to new results (presented here) obtained using the supersymmetric approach to the N = 2 case. We demonstrate that this ménageà trois of different approaches leads to identical results. Remarkable relations between apparently different conformal field theories (CFTs) are thereby obtained. We further establish a connection between the random Dirac fermion problem and the c = −2 theory of dense polymers. The presence of the c = −2 theory may be seen in all three different treatments of the disorder. PACS: 72.15.Rh, 71.30.+h

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“…Combining the global N = 4 algebra (2.35) with the full Virasoro algebra (2.12) and affine SU (2) × SU (2) × U (1), (2.15), (2.16), (2.21) (in the worldsheet BRST cohomology and using the freedom of picture changing [7]) leads to the so called "large" N = 4 superconformal algebra [8,9]. This chiral algebra is generated by a spin-2 stress tensor (whose modes are L n , n ∈ Z), four spin-3/2 fields (with modes G ij r , r ∈ Z + 1/2), seven spin-1 currents (with modes T a n , R a n , α n ), and four spin-1/2 fermions (with modes Γ ij r ).…”

Section: Spacetime Propertiesmentioning

confidence: 99%

“…To construct the spacetime supercharges we introduce the 32 worldsheet spin fields S α , α = 1, ..., 32, which satisfy [7]:…”

Section: Spacetime Propertiesmentioning

confidence: 99%