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Recent questions tagged duality

A duality is a sort-of equivalence between two objects or theories under a certain condition. Very useful in QFT and string theory.

List of some dualities in physics:

S-duality (in string theory and quantum field theory)

Involves the reciprocal of the coupling constant. Theory A is said to be S-dual to Theory B if Theory A with coupling constant $g$ is the equivalent of Theory B with coupling constant $\frac1g$. In string theory, this is the same as negating the dilaton field, as $g=\langle e^{\phi}\rangle$.

T-duality (in string theory)

Involves the reciprocal of the compactification radius. Theory A is said to be T-dual to Theory B if Theory A with compactification radius $R$ is the equivalent of Theory B with compactification radius $\frac{\alpha'}{R}$, which is simply $\frac1R$ if we chose to use natural units where we let $\ell_s=1$.

AdS/CFT (in string theory = conformal field theory, for example. However, there are generalisations which also include AdS/QCD, AdS/CMT, etc.)

Relates a string theory or quantum gravitational theory in a certain AdS spacetime to one conformal field theory on the conformal boundary of the AdS spacetime. Prominent examples include BFSS Matrixz theory and Matrix string theoryies (IIA and HE).

Electromagnetic duality (in a whole lot of stuff)

Self-explanatory. Dualities which are like EM. In EM, field - strengths can be described by the electric field part, whereas the dual field strengths can be described by the magnetic field part. Useful even in string theory, where $Dp$ - branes are EM-dual to $D(6-p)$ - branes.