Old dualities and new anomalies

Beta functions for the duality-invariant sigma model

“…This, together with a general analysis of the Weyl anomaly, gives the complete O(d, d)−invariant target space equations to lowest order in α , which agree with the low-energy effective action constructed by Maharana and Schwarz in [34]. This result generalizes the earlier works of [14,15] by including the external B-field and Kaluza-Klein gauge vectors and provides a positive check on the viability of the sigma model [9] to determine higher order α corrections.…”

“…Having reviewed the necessary tools to extract target space equations from a given string sigma model, we turn in this section to the main subject of this paper. We shall compute the one-loop β−functions of the O(d, d)−invariant sigma model recently discussed in [9]. This, together with a general analysis of the Weyl anomaly, gives the complete O(d, d)−invariant target space equations to lowest order in α , which agree with the low-energy effective action constructed by Maharana and Schwarz in [34].…”

“…Here we aim to circumvent the need for a two-step procedure by employing a duality invariant worldsheet theory that is directly adapted to the dimensional reduction and is manifestly O(d, d, R) invariant. This worldsheet action, which generalizes a formulation due to Tseytlin [5,6], was originally given by Schwarz and Sen [7] and more recently re-derived in [8,9]. In particular in [9] it was shown that this model is a consistent truncation of the standard worldsheet theory in which internal momentum and winding modes are set to zero, being the worldsheet counterpart of taking the target space fields to be independent of d coordinates.…”

“…This worldsheet action, which generalizes a formulation due to Tseytlin [5,6], was originally given by Schwarz and Sen [7] and more recently re-derived in [8,9]. In particular in [9] it was shown that this model is a consistent truncation of the standard worldsheet theory in which internal momentum and winding modes are set to zero, being the worldsheet counterpart of taking the target space fields to be independent of d coordinates. Moreover, it was shown that the duality symmetries become anomalous quantum mechanically due to the presence of chiral bosons.…”

The generalized Bergshoeff-de Roo identification. Part II

“…There are methods based on explicit reductions, such as cosmological [10,11], circle [12][13][14][15][16][17] and intermediate [18][19][20] compactifications. There is also a duality covariant sigma-model approach to higher derivatives [21]. Here we will focus on higher derivatives in DFT, for which originally there were two alternatives.…”