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JamalS
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In the context of bosonic string theory, the ground state with no oscillator excited, has a mass,

$$M^2 = -\frac{1}{\alpha'}\frac{D-2}{6}$$

where $\alpha'$ is the Regge slope, satisfying $\alpha' = 1/2\pi T$, where $T$ is the tension of the spring, and $D$ are the spacetime dimensions. It seems it has an imaginary mass (providing $D\geq 3$). You may have also heard this particle is unnatural because it propagates faster than $c$.


Let's go back to quantum field theory for a moment. Generally, the mass squared is simply the term that appears in the quadratic part of the Lagrangian, i.e.

$$M^2 = \frac{\partial^2 V(\phi)}{\partial \phi^2} \biggr\rvert_{\phi = 0}$$

Hence, if $M^2 < 0$, we can interpret that as the fact that we are expanding around a maximum of the potential for a tachyon field (see second derivative test). With this perspective, the Higgs field can also be viewed as a tachyon. As D. Tong states, it is unfortunate that bosonic string theory sits at this unstable point in the potential of the tachyon field. To date, we still don't know of a minimum of $V(\phi)$. (One can compute higher order corrections, and find a minimum, but then the next correction destabilizes the minimum again.)

  So it seems the issue in string theory is not causality; the issues with the tachyon maycausality, rather they run much deeper.

In the context of bosonic string theory, the ground state with no oscillator excited, has a mass,

$$M^2 = -\frac{1}{\alpha'}\frac{D-2}{6}$$

where $\alpha'$ is the Regge slope, satisfying $\alpha' = 1/2\pi T$, where $T$ is the tension of the spring, and $D$ are the spacetime dimensions. It seems it has an imaginary mass (providing $D\geq 3$). You may have also heard this particle is unnatural because it propagates faster than $c$.


Let's go back to quantum field theory for a moment. Generally, the mass squared is simply the term that appears in the quadratic part of the Lagrangian, i.e.

$$M^2 = \frac{\partial^2 V(\phi)}{\partial \phi^2} \biggr\rvert_{\phi = 0}$$

Hence, if $M^2 < 0$, we can interpret that as the fact that we are expanding around a maximum of the potential for a tachyon field (see second derivative test). With this perspective, the Higgs field can also be viewed as a tachyon. As D. Tong states, it is unfortunate that bosonic string theory sits at this unstable point in the potential of the tachyon field. To date, we still don't know of a minimum of $V(\phi)$. (One can compute higher order corrections, and find a minimum, but then the next correction destabilizes the minimum again.)

  So it seems the issue in string theory is not causality; the issues with the tachyon may run much deeper.

In the context of bosonic string theory, the ground state with no oscillator excited, has a mass,

$$M^2 = -\frac{1}{\alpha'}\frac{D-2}{6}$$

where $\alpha'$ is the Regge slope, satisfying $\alpha' = 1/2\pi T$, where $T$ is the tension of the spring, and $D$ are the spacetime dimensions. It seems it has an imaginary mass (providing $D\geq 3$). You may have also heard this particle is unnatural because it propagates faster than $c$.


Let's go back to quantum field theory for a moment. Generally, the mass squared is simply the term that appears in the quadratic part of the Lagrangian, i.e.

$$M^2 = \frac{\partial^2 V(\phi)}{\partial \phi^2} \biggr\rvert_{\phi = 0}$$

Hence, if $M^2 < 0$, we can interpret that as the fact that we are expanding around a maximum of the potential for a tachyon field (see second derivative test). With this perspective, the Higgs field can also be viewed as a tachyon. As D. Tong states, it is unfortunate that bosonic string theory sits at this unstable point in the potential of the tachyon field. To date, we still don't know of a minimum of $V(\phi)$. (One can compute higher order corrections, and find a minimum, but then the next correction destabilizes the minimum again.) So it seems the issue in string theory is not causality, rather they run much deeper.

Source Link
JamalS
  • 19.5k
  • 6
  • 59
  • 107

In the context of bosonic string theory, the ground state with no oscillator excited, has a mass,

$$M^2 = -\frac{1}{\alpha'}\frac{D-2}{6}$$

where $\alpha'$ is the Regge slope, satisfying $\alpha' = 1/2\pi T$, where $T$ is the tension of the spring, and $D$ are the spacetime dimensions. It seems it has an imaginary mass (providing $D\geq 3$). You may have also heard this particle is unnatural because it propagates faster than $c$.


Let's go back to quantum field theory for a moment. Generally, the mass squared is simply the term that appears in the quadratic part of the Lagrangian, i.e.

$$M^2 = \frac{\partial^2 V(\phi)}{\partial \phi^2} \biggr\rvert_{\phi = 0}$$

Hence, if $M^2 < 0$, we can interpret that as the fact that we are expanding around a maximum of the potential for a tachyon field (see second derivative test). With this perspective, the Higgs field can also be viewed as a tachyon. As D. Tong states, it is unfortunate that bosonic string theory sits at this unstable point in the potential of the tachyon field. To date, we still don't know of a minimum of $V(\phi)$. (One can compute higher order corrections, and find a minimum, but then the next correction destabilizes the minimum again.)

So it seems the issue in string theory is not causality; the issues with the tachyon may run much deeper.