Green-Schwarz Strings in TsT-transformed backgrounds

Abstract

We consider classical strings propagating in a background generated by a sequence of TsT transformations. We describe a general procedure to derive the Green-Schwarz action for strings. We show that the U(1) isometry variables of the TsT-transformed background are related to the isometry variables of the initial background in a universal way independent of the details of the background. This allows us to prove that strings in the TsT-transformed background are described by the Green-Schwarz action for strings in the initial background subject to twisted boundary conditions. Our construction implies that a TsT transformation preserves integrability properties of the string sigma model. We discuss in detail type IIB strings propagating in the γ i -deformed AdS 5 ×S 5 space-time, find the twisted boundary conditions for bosons and fermions, and use them to write down an explicit expression for the monodromy matrix. We also discuss string zero modes whose dynamics is governed by a fermionic generalization of the integrable Neumann model. *

The AdS5× S5superstring in light-cone gauge and its Bethe equations

“…This should be relevant for the study of γ -deformed models [35,36] which are known to be related to Green-Schwarz superstrings in AdS 5 × S 5 subject to twisted boundary conditions [34,36]. The twisting effectively corresponds to a non-vanishing (and non-integer) mode number in the expansion around plane wave limits.…”

“…On the other hand, as was discussed in [28], to impose the light-cone gauge it is convenient to use fields neutral under these two U(1) subgroups. This requires us to redefine the fermions by performing a similarity transformation of the matrix g(θ) [34] 9 . The result of this transformation is equivalent to choosing a different coset element from the start, namely we choose the element to be of the form …”

Finite-size effects from giant magnons

“…Strictly speaking, the original Green-Schwarz action presented in [50] contains fermions which are charged under the U(1) transformations generated by the shifts of t and φ. However, it is possible to redefine the fermions and make them neutral, see [48,51] for details.…”

Towards the All-Loop WorldsheetSMatrix forAdS3×S3×TBorsato1, Sax2, Sfondrini3 et al. 2014Phys. Rev. Lett.8421750View full textAdd to dashboardCite

“…To carry out this procedure explicitly we need to redefine the fermions θ I to make them neutral under the U(1) isometries generated by t and ϕ translations [36]. This yields a nonlocal piece in the supercharges.…”