u/_4bdn_fruit_

I'm a little confused about spontaneous symmetry breaking. My understanding is that a universe initially in a symmetrical state (represented by a ball on the top of a Mexican hat) can eventually roll down to one of the points on the brim, and all the continuous points on the brim represent a possible point the universe can settle into. In terms of the physical constants, does it matter which one of those points (vacua) the universe settles into? Or are the physical constants and particle masses the same regardless?

To clarify, I'm asking this because the concept of vacuum states is also related to string theory, and the different vacuum states on the string theory landscape lead to different physical constants. Is this not the case when we're just talking about spontaneous symmetry breaking in a non-string theory sense?

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?

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?

In string theory discussions, I often hear about solutions that are unstable and solutions that are inconsistent with quantum gravity (such as those in the swampland or those with the wrong number of dimensions). My understanding is that these are two separate categories. Unstable solutions represent the "slanted" regions of the landscape that will decay until they reach a stable vacuum, and these unstable regions are still valid parts of the theory. But solutions or geometries that are inconsistent with quantum gravity are not allowed to exist, even as transient states. At the same time, the stability or instability of a solution (like the case with the de Sitter vacua) can influence whether the solution is consistent with string theory. Is my understanding correct?

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?