### Ghost D-Branes and Renormalization

Catch a very interesting discussion over at Cosmic Variance of a paper by Evans, Morris and Rosten, relating Morris’s Exact Renormalization Group for large-$N$ $SU(N)$ Yang Mills to the “Ghost D-brane” proposal of Okuda and Takayanagi.

The claim is that, by embedding $SU(N)$ Yang-Mills in a larger (nonunitary) theory, whose gauge groups is the supergroup $SU(N|N)$, spontaneously broken to $SU(N)\times SU(N)$, one can produce a gauge-invariant Pauli-Villars regulator, with which to implement the Exact RG. The latter theory, in turn, is what Okuda and Takyanagi argue is the world-volume theory of a stack of D-branes and ghost D-branes.

When the gauge symmetry is unbroken, the $SU(N|M)$ theory is equivalent to $SU(N-M)$, as far as computing gauge-invariant observables. In particular, there is a perfect cancellation of diagrams for $N=M$.

Turning on a nonzero Higgs VEV (separating the D-branes from the ghost D-branes) provides a cutoff for the original $SU(N)$ theory. Above the scale of the Higgs VEV, you get zero; far below it, the “original” $SU(N)$ degrees of freedom decouple from the ghost $SU(N)$.

Evans *et al* propose and AdS/CFT geometry realization of this idea, with the hope of connecting, in a explicit way, the “holographic RG” (evolution in the radial coordinate of AdS) with the “exact RG” of Morris.

Anyway, Takuya Okuda is over there, fielding questions, so take advantage …

Posted by distler at January 28, 2006 1:29 AM
## Re: Ghost D-Branes and Renormalization

Hi Jacques or Takuya,

do you actually understand why is the regularization using the supergroup connected with the appearance of the holographic fifth dimension? I have no clue. The simple reason why I have no clue is that so far I did not consider the choice of a gauge-invariant regulator to be more than a minor technical challenge for gauge theory, while holography is a shocking and mysterious feature of gauge theories.

Thanks,

Lubos