On divergences in non-minimal N=4 conformal supergravity

We review the question of quantum consistency of N=4 conformal supergravity in 4 dimensions. The UV divergences and anomalies of the standard ("minimal") conformal supergravity where the complex scalar $\phi$ is not coupled to the Weyl graviton kinetic term can be cancelled by coupling this theory to N=4 super Yang-Mills with gauge group of dimension 4. The same turns out to be true also for the "non-minimal" N=4 conformal supergravity with the action (recently constructed in arXiv:1609.09083) depending on an arbitrary holomorphic function $f(\phi)$. The special case of the "non-minimal" conformal supergravity with $f= e^{2\phi}$ appears in the twistor-string theory. We show that divergences and anomalies do not depend on the form of the function $f$ and thus can be cancelled just as in the "minimal" $f=1$ case by coupling the theory to four N=4 vector multiplets.Comment: 6 pages. v2: minor comment and references adde

Born-Infeld action, supersymmetry and string theory

We review and elaborate on some aspects of Born-Infeld action and its supersymmetric generalizations in connection with string theory. Contents: BI action from string theory; some properties of bosonic D=4 BI action; N=1 and N=2 supersymmetric BI actions with manifest linear D=4 supersymmetry; four-derivative terms in N=4 supersymmetric BI action; BI actions with `deformed' supersymmetry from D-brane actions; non-abelian generalization of BI action; derivative corrections to BI action in open superstring theory.Comment: 37 pages, harvmac, contribution to Yuri Golfand memorial volume; misprints correcte

Magnetic backgrounds and tachyonic instabilities in closed string theory

We discuss some aspects of closed superstrings in Melvin-type magnetic backgrounds. A 2-parameter family of such NS-NS backgrounds are exactly solvable as weakly coupled string models with the spectrum containing tachyonic modes. Magnetic field allows one to interpolate between free superstring theories with periodic and antiperiodic boundary conditions for the space-time fermions around some compact direction, and, in particular, between type 0 and type II string theories. Using ``9-11'' flip, this interpolation can be extended to M-theory and may be used to study the issue of tachyon in type 0 string theory. We review, following hep-th/0104238, related duality proposals, and, in particular, consider a description of type 0 theory in terms of M-theory in a curved magnetic flux background in which the type 0 tachyon appears to correspond to a state in $d=11$ supergravity fluctuation spectrum.Comment: 12 pages, latex. Contribution to the proceedings of the 10-th Tohwa International Symposium on String Theory, Fukuoka, Japan, July 3-7, 2001; v2: references adde