# 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.

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