- #1
rbwang1225
- 118
- 0
Given an action for a 5-brance
##S=\int d^6x\left[\sqrt{-g}{1\over
{4\partial_r a\partial^r a}}\partial_ma(x)F^{*mnl}F_{nlp}\partial^pa(x)+
\sqrt{-\det(g_{mn}+i\tilde F_{mn})}\right],##
where ##x^m## ##(m=0,1...,5)## are local coordinates of the worldvolume, ##g_{mn}(x)=\partial_mX^M(x)g_{MN}\partial_nX^N(x)## is a worldvolume metric
induced by embedding into curved target space with the metric ##g_{MN}(X)## parametrized by coordinates ##X^M## ##(M,N=0,...,D-1)##; ##F_{mnl}=2(\partial_{l}A_{mn}+ \partial_{m}A_{nl}+\partial_{n}A_{lm})## is the field strength of an antisymmetric worldvolume gauge field ##A_{mn}(x)##;
##g=\det{g_{mn}}##; ##F^{*lmn}## is the dual field strength:
$$ F^{*lmn}={1\over {6\sqrt{-g}}} \varepsilon^{lmnpqr}F_{pqr} $$
and
$$\tilde
F_{mn}\equiv{1\over{\sqrt{(\partial a)^2}}}F^{*}_{mnl}\partial^la(x).$$
The scalar field ##a(x)## ensures manifest ##d=6## covariance of the model and is completely auxiliary.
My question is how do I reduce it to a 1-brance, i.e., a string?
Is there any standard procedure for this kind of problem?
Any devices would be very appreciated.
##S=\int d^6x\left[\sqrt{-g}{1\over
{4\partial_r a\partial^r a}}\partial_ma(x)F^{*mnl}F_{nlp}\partial^pa(x)+
\sqrt{-\det(g_{mn}+i\tilde F_{mn})}\right],##
where ##x^m## ##(m=0,1...,5)## are local coordinates of the worldvolume, ##g_{mn}(x)=\partial_mX^M(x)g_{MN}\partial_nX^N(x)## is a worldvolume metric
induced by embedding into curved target space with the metric ##g_{MN}(X)## parametrized by coordinates ##X^M## ##(M,N=0,...,D-1)##; ##F_{mnl}=2(\partial_{l}A_{mn}+ \partial_{m}A_{nl}+\partial_{n}A_{lm})## is the field strength of an antisymmetric worldvolume gauge field ##A_{mn}(x)##;
##g=\det{g_{mn}}##; ##F^{*lmn}## is the dual field strength:
$$ F^{*lmn}={1\over {6\sqrt{-g}}} \varepsilon^{lmnpqr}F_{pqr} $$
and
$$\tilde
F_{mn}\equiv{1\over{\sqrt{(\partial a)^2}}}F^{*}_{mnl}\partial^la(x).$$
The scalar field ##a(x)## ensures manifest ##d=6## covariance of the model and is completely auxiliary.
My question is how do I reduce it to a 1-brance, i.e., a string?
Is there any standard procedure for this kind of problem?
Any devices would be very appreciated.