Deformation of Script N = 4 super Yang–Mills theory in graviphoton background

Abstract

We study deformation of N = 4 super Yang-Mills theory from type IIB superstrings with D3-branes in the constant R-R background. We compute disk amplitudes with one graviphoton vertex operator and investigate the zero-slope limit of the amplitudes. We obtain the effective action deformed by the graviphoton background, which contains the one defined in non(anti)commutative N = 1 superspace as special case. The bosonic part of the Lagrangian gives the Chern-Simons term coupled with the R-R potential. We study the vacuum configuration of the deformed Lagrangian and find the fuzzy sphere configuration for scalar fields.

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“…Prepotential of non(anti)commutative gauge theory with singlet deformation was also discussed in [20]. Using string theory technique, further extension to the N = 4 gauge theory in the R-R 5-form graviphoton background was investigated [23], but their instanton solutions are not yet studied so far. Recently its gravity dual has been proposed in [24].…”

“…In type IIB theory, for example, there are R-R 3-forms (and its dual), which correspond to the backgrounds F (αβ) [AB] and F [αβ](AB) , denoted as (S,A) and (A,S) type deformations [23]. Here A, B = 1, .…”

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“…In [18,19] we discussed the deformation of N = 2 and N = 4 super Yang-Mills theories in the R-R background field strength of the form F αβAB , where α and β label the spinor indices of (Euclidean) space-time and A and B are internal spinor indices. We classify the field strength into four types F (αβ)(AB) , F [αβ](AB) , F (αβ) [AB] and F [αβ] [AB] .…”

“…In [18], we studied the first order correction to N = 2 super Yang-Mills action from the (S,S)-type background with fixed (2πα ′ ) 3/2 F. We showed that deformed theory agrees with N = 2 super Yang-Mills theory on non(anti)commutative N = 2 harmonic superspace [11 -13]. In [19], we studied the first order correction to N = 4 super Yang-Mills theory in (S,S)-type background with fixed (2πα ′ ) 3/2 F. By restricting the deformation parameter to the special case, the deformed Lagrangian is reduced to the one in non(anti)commutative N = 1 superspace. Therefore it is natural to think that the (S,S)-type deformation with fixed (2πα ′ ) 3/2 F corresponds to the non(anti)commutative deformation of N (≤ 4) extended superspace at full order in deformation parameter.…”

Nonanticommutativity in the presence of a boundary

“…Such deformations are realised on the worldvolume of D-branes in RR backgrounds [22,23,24,25,26], and the gravity dual of such a field theory has been constructed in [27]. Also, a graviphoton background gives rise to a noncommutativity between spacetime and superspace coordinates [23,28,29,30,31]. Noncommutative deformations generated by the N S − N S and graviphoton backgrounds do not break any supersymmetry.…”