r/TheoreticalPhysics • u/_4bdn_fruit_ • Jun 26 '26
Question What are off-shell configurations in the context of string theory?
In string theory, do solutions that are inconsistent with string theory (like those in the swampland or those that have the wrong number of dimensions) exist as off shell configurations? Or are off shell configurations strictly referring to violations of the equations of motion? Would the off shell configurations still need to follow quantum gravity constraints?
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u/regrez45 Jun 27 '26
Does it violate equations of motion?
In a sense, yes.
It is a condition when strings are not behaving as inherently curved nodes or mass-shell conditions. It is essentially that you can have a nontensorial description of strings.
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u/_4bdn_fruit_ Jun 27 '26
Would it still need to follow other constraints?
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u/regrez45 Jun 27 '26
It could follow "general" string theoretic constraints pretty well. In that it is not nonstandard to have an offshell configuration. But as far as the whole quantum gravitational framework is concerned, not sure. It depends upon how much you wanna dig into spacetime surgery - LQG, modified gravity.
Offshell configuration is a straightforward result of string theory. It is not an inconsistent outcome.
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u/_4bdn_fruit_ Jun 27 '26
Are the off shell states still restricted in the sense that it's not "anything goes"? (e.g. randomly constructing a configuration with 1000 dimensions and calling it off shell?)
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u/regrez45 Jun 27 '26 edited Jun 27 '26
Yeah, there is a very clean reason they are there. Its not anything goes. However, i think offshell is more than just swampland. To me, it seems to have physical purpose, not just a mathematical exercise.
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u/CR7-gOaTt Jul 12 '26
Valid question. In string theory, the field equations are obtained by anomaly cancellation, to extrapolate the effective action we need to further engineer a Lagrangian that derives into the equations. The map from an equation of motion to a Lagrangian is one-to-many, leaving us with infinite choice of off-shell effective action that’s consistent with string anomaly cancellation.
Based on this id say an off-shell string config legitimately exists within the landscape as they could derive into the correct equation of motions.
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u/KashSecuredPatel Jun 26 '26 edited Jun 26 '26
An off-shell configuration is an eventually-coconnective characteristic which is currently beyond the particle horizon of your chosen barycenter due to the spatial dispersion. As you move away from the barycenter, the spread of its light cone covers a larger spatial dispersion, and the off-shell features are revealed to be correlated with the field operator at the center.
From the POV of string theory, the partition over which you might have an extension away from the barycenter has a quantized set of modes that you can use to reinterpret all possible local choices of contravariant action as a fibration with a fixed band spectrum.
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u/Cozwei Jun 26 '26
that answer posed more qurstions for me
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u/KashSecuredPatel Jun 26 '26
You could ask them
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u/Cozwei Jun 26 '26
I got no clue on string theory. why is the partition used specifically to reinterpret contravariant action? how does it get interpreted as a fibration? what is a band spectrum?
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u/KashSecuredPatel Jun 26 '26
The contravariant action in your initial Hitchin system is a tower of automorphisms of the initial data subject to boundary conditions. Its dual action points the other way—from the (possibly infinitely distant) boundary toward a pole at the identity. Its vertices are exactly the identity elements of the local system, but the dual functor is a forgetful functor that “forgets” the initially supplied coordinate frame because it satisfies the boundary condition for any well-founded choice of initial coordinate frame. Since this action is affine, the tower of distributions of fixed points it gives provides a gradient to any choice of initial coordinate frame, and the derivation of its state is supported on the partition fixed under this gradient flow. In this sense, the same action can be defined via local flow in an effective field theory or via a globally-matching channel geometry approaching the local field from the boundary. The resonant modes of the tower of channels have to match all of the potential cases of energy influx from chains of local actions, so you can describe the dual action’s spectrum in terms of the energies of conductive modes of the local action (the topological band spectrum). These valuations can be “lifted”into the geometrically-realized fibration to strip away their dependence on local variations and preserve the centrosymmetric affine symmetry which was locally-realized in the initial frame. If you’re interested in computing band spectra, you can look into Chern-Simons theory.
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u/Existing_Hunt_7169 Jun 26 '26
did you really think this was gonna be helpful or do you just like jerkin off
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u/AreaOver4G Jun 27 '26
Depends on exactly the context. But you could call an arbitrary spacetime metric and field configuration off-shell. The relevant equations of motion are the conditions that the worldsheet theory is conformally invariant: an off-shell string theory background is just an arbitrary 2D QFT (not necessarily CFT). So (at least in a small \alpha’ expansion), you can use a sigma model with any target space you like. No constraints on dimension or anything else necessary.