Minimal gauge invariant couplings at order $$\alpha '^3$$: NS–NS fields
Mohammad R. Garousi
Abstract
Abstract Removing the field redefinitions, the Bianchi identities and the total derivative freedoms from the general form of gauge invariant NS–NS couplings at order $$\alpha '^3$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>α</mml:mi> <mml:mrow> <mml:mo>′</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:msup> </mml:math> , we have found that the minimum number of independent couplings is 872. We find that there are schemes in which there is no term with structures $$R,\,R_{\mu \nu },\,\nabla _\mu H^{\mu \alpha \beta }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>R</mml:mi> <mml:mo>,</mml:mo> <mml:mspace/> <mml:msub> <mml:mi>R</mml:mi> <mml:mrow> <mml:mi>μ</mml:mi> <mml:mi>ν</mml:mi> </mml:mrow> </mml:msub> <mml:mo>,</mml:mo> <mml:mspace/> <mml:msub> <mml:mi>∇</mml:mi> <mml:mi>μ</mml:mi> </mml:msub> <mml:msup> <mml:mi>H</mml:mi> <mml:mrow> <mml:mi>μ</mml:mi> <mml:mi>α</mml:mi> <mml:mi>β</mml:mi> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> , $$ \nabla _\mu \nabla ^\mu \Phi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>∇</mml:mi> <mml:mi>μ</mml:mi> </mml:msub> <mml:msup> <mml:mi>∇</mml:mi> <mml:mi>μ</mml:mi> </mml:msup> <mml:mi>Φ</mml:mi> </mml:mrow> </mml:math> . In these schemes, there are sub-schemes in which, except one term, the couplings can have no term with more than two derivatives. In the sub-scheme that we have chosen, the 872 couplings appear in 55 different structures. We fix some of the parameters in type II supersting theory by its corresponding four-point functions. The coupling which has term with more than two derivatives is constraint to be zero by the four-point functions.