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People sometimes talk about on-shell symmetries: symmetries of the equations of motion or the S-matrix, which do not hold off-shell (i.e. at the level of the action, path integral, correlators, etc). Electric-magnetic duality transformations $$ \begin{aligned} F &\rightarrow \cos(\theta)\,F - \sin(\theta)\,\star F \\ \star F &\rightarrow \sin(\theta)\,F + \cos(\theta)\,\star F \end{aligned} $$ are an example of this. These transformations leave the equations of motion and the S-matrix invariant (with a corresponding selection rule), so they would qualify as a symmetry.

However, this symmetry is usually broken by non-perturbative effects (e.g. monopoles), to which the usual S-matrix is insensitive. In addition, it is well known that dualities are not symmetries of the full theory but instead a better understood as a change in our description of the physics. For instance duality transformations relate the partition function of the theory at different values of the coupling (see this paper for an example).

People sometimes talk about on-shell symmetries: symmetries of the equations of motion or the S-matrix, which do not hold off-shell (i.e. at the level of the action, path integral, correlators, etc). Electric-magnetic duality transformations $$ \begin{aligned} F &\rightarrow \cos(\theta)\,F - \sin(\theta)\,\star F \\ \star F &\rightarrow \sin(\theta)\,F + \cos(\theta)\,\star F \end{aligned} $$ are an example of this. These transformations leave the equations of motion and the S-matrix invariant (with a corresponding selection rule), so they would qualify as a symmetry.

However, this symmetry is usually broken by non-perturbative effects (e.g. monopoles). In addition, it is well known that dualities are not symmetries of the full theory but instead a better understood as a change in our description of the physics. For instance duality transformations relate the partition function of the theory at different values of the coupling (see this paper for an example).

People sometimes talk about on-shell symmetries: symmetries of the equations of motion or the S-matrix, which do not hold off-shell (i.e. at the level of the action, path integral, correlators, etc). Electric-magnetic duality transformations $$ \begin{aligned} F &\rightarrow \cos(\theta)\,F - \sin(\theta)\,\star F \\ \star F &\rightarrow \sin(\theta)\,F + \cos(\theta)\,\star F \end{aligned} $$ are an example of this. These transformations leave the equations of motion and the S-matrix invariant (with a corresponding selection rule), so they would qualify as a symmetry.

However, this symmetry is usually broken by non-perturbative effects (e.g. monopoles), to which the usual S-matrix is insensitive. In addition, it is well known that dualities are not symmetries of the full theory but instead a better understood as a change in our description of the physics. For instance duality transformations relate the partition function of the theory at different values of the coupling (see for instance this paper).

People sometimes talk about on-shell symmetries: symmetries of the equations of motion or the S-matrix, which do not hold off-shell (i.e. at the level of the action, path integral, correlators, etc). Electric-magnetic duality transformations $$ \begin{aligned} F &\rightarrow \cos(\theta)\,F - \sin(\theta)\,\star F \\ \star F &\rightarrow \sin(\theta)\,F + \cos(\theta)\,\star F \end{aligned} $$ are an example of this. These transformations leave the equations of motion and the S-matrix invariant (with a corresponding selection rule), so they would qualify as a symmetry.

However, this symmetry is usually broken by non-perturbative effects (e.g. monopoles), to which the usual S-matrix is insensitive. In addition, it is well known that dualities are not symmetries of the full theory but instead a better understood as a change in our description of the physics. For instance duality transformations relate the partition function of the theory at different values of the coupling (see this paper for an example).

People sometimes talk about on-shell symmetries: symmetries of the equations of motion or the S-matrix, which do not hold off-shell (i.e. at the level of the action, path integral, correlators, etc). Electric-magnetic duality transformations $$ \,\,\,\,\,F \rightarrow \cos(\theta)\,F - \sin(\theta)\,\star F \\ \star F \rightarrow \sin(\theta)\,F + \cos(\theta)\,\star F $$ are an example of this. These transformations leave the equations of motion and the S-matrix invariant (with a corresponding selection rule), so they would qualify as a symmetry.

However, this symmetry is usually broken by non-perturbative effects (e.g. monopoles), to which the usual S-matrix is insensitive. In addition, it is well known that dualities are not symmetries of the full theory but instead a better understood as a change in our description of the physics. For instance duality transformations relate the partition function of the theory at different values of the coupling (see for instance this paper).

People sometimes talk about on-shell symmetries: symmetries of the equations of motion or the S-matrix, which do not hold off-shell (i.e. at the level of the action, path integral, correlators, etc). Electric-magnetic duality transformations $$ \begin{aligned} F &\rightarrow \cos(\theta)\,F - \sin(\theta)\,\star F \\ \star F &\rightarrow \sin(\theta)\,F + \cos(\theta)\,\star F \end{aligned} $$ are an example of this. These transformations leave the equations of motion and the S-matrix invariant (with a corresponding selection rule), so they would qualify as a symmetry.

However, this symmetry is usually broken by non-perturbative effects (e.g. monopoles), to which the usual S-matrix is insensitive. In addition, it is well known that dualities are not symmetries of the full theory but instead a better understood as a change in our description of the physics. For instance duality transformations relate the partition function of the theory at different values of the coupling (see for instance this paper).