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3

Since S-duality relates a theory at weak coupling to a theory at strong coupling it is in general very hard to rigorously prove that two theories are dual. However, the basic arguments for why it should hold in string theory are given in many text books, see eg chapter 14 in Polchinski or Becker, Becker, Schwarz chapter 8. Here I will just sketch how the ...

7

One shouldn't imagine the T-duality between the two heterotic strings to be a $Z_2$ group, like in the case of type II string theories' T-duality. In type II string theory, there is only one relevant scalar field, the radius of the circle producing T-duality, and it gets reverted $R\to 1/R$ under T-duality. In the heterotic case, it's more complicated ...

0

I just found that my question (2) is trivially easy and that indeed it is: $$\begin{array}{l} m = \sqrt {\frac{{2\pi T}}{{{c_0}}}\left( {B + {{\tilde N}_{II}} - {a_B} - {{\tilde a}_{II}}} \right)} \\ {\rm{ }} = \sqrt {\frac{{2\pi T}}{{{c_0}}}\left( {B + {{\tilde N}_{II}} - 1 - {{\tilde a}_{II}}} \right)} \end{array}$$ This is because: ...

0

Here is my solution. For the Ramond Ramond Sector, $${m_\rm{I}} = \frac{{\left[ {\hat a_ + ^\mu ,\hat{\tilde a}_ + ^\nu } \right]}}{2}{m_{{\rm{IIB}}}}$$ For the Neveu-Schwarz Neveu-Schwarz Sector, $${m_\rm{I}} = \frac{{\left[ {\hat d_ {-1/2} ^\mu ,\hat{\tilde d}_{-1/2} ^\nu } \right]}}{2}{m_{{\rm{IIB}}}}$$ For the Ramond Neveu-Schwarz Sector or the ...

2

Hagedorn spectrum just means that the density of states varies exponentially with the energy/mass. $m^2$ (asymptotically) given by the "level" (N) of the state (upto a sqrt). The number of states at level $N$ corresponds to the possible partitions of $N$ into different oscillator modes. That means that the number of states at level $N$ will increase ...

1

I would really recommend a study in QFT before going on to study SUSY. QFT has many quirks that make supersymmetry a very interesting expansion of the regular framework. You'd miss out on all that as you just had to believe the facts presented w/o following the thought that lead to the results in detail. On the Mathematical level you will need Grassmann ...

3

If you spend some time looking in detail at the arguments that string theory requires supersymmetry, you'll find that they are not watertight. (How could they be, since we still can't say/don't know precisely what string theory is?) Basically, some string theorists argue that that the usual classification depends too strongly on choosing nearly trivial ...

1

p-adic strings or the adelic approach created by B.Dragovich don't require SUSY at all. At least, not the usual SUSY symmetry... Non-critical string theory, the so-called Liouville theory, is based on the hypothesis of non-imposing the condition that critical strings with fermions (superstrings) impose on the space-time dimension due to internal ...

0

Generally, in the MSSM one works with the "minimal flavor violation" paradigm that states that all flavor violation originates in the SM Yukawa sector. This paradigm is ad hoc, but explains why no huge SUSY contributions to FCNC observables are seen. There are models that go beyond minimal flavor violation and some that give an explanation for the ...

0

A working group from the Intensity frontier has prepared two families of parameterized MSSM benchmark models in the run-up to Snowmass on the Mississippi (a 2013 process for trying to understand and guide where US high energy physics is heading in the next 10ish years or so). See also their summary talk from the April 2013 Intensity Frontier workshop at ...

1

There are lots of questions here! I think I can answer at least some... First of all, you are aware that the fields in $W$ and $K$ are superfields? These contain the entire supermultiplet, so they must be complex in general. This is a short entry but it links to others: http://en.wikipedia.org/wiki/Superfield As mentioned by Jose in his comment, the ...

4

There is a standard paradigm for thinking about the new physics that lies beyond the standard model, at higher and higher energies: weak-scale supersymmetry, grand unification, string theory. The purpose of weak-scale supersymmetry is to stabilize weak-scale physics (i.e. everything we know about) against quantum corrections. Grand unification can explain ...

1

"Falsifying supersymmetry" is a phrase that has to be properly qualified. Our ability to falsify with experiment is limited. We can rule out the existence of supersymmetry only at accessible energy/distance/density scales. LHC, for example, is not able to resolve physics at distance scales much smaller than $\frac{\hbar c}{7\mbox{ TeV}} \simeq ... 0 Actually, no. The supersymmetric transformations are elegant and simple ways of extending the Bosonic String theory to fermions, but if supersymmetry is falsified somehow, then maybe all of the discovered superstring theory would have to be discarded, but a new one may emerge... It would just use different supersymmetric transformations with different ... 3 The NS-NS sector is the same in type IIA and IIB, but the R-NS and NS-R sectors differ. The type IIA theory is non-chiral, so the R-NS and NS-R fields transform in$\mathbf{8}_s \otimes \mathbf{8}_v$and$\mathbf{8}_v \otimes \mathbf{8}_s'$, where$\mathbf{8}_s$and$\mathbf{8}_s'$are the two eight-dimensional spinor representations of$SO(8)$. Type IIB, on ... 6 Noncompact internal symmetries – and R-symmetry is an internal symmetry (it doesn't transform positions in the spacetime) – are unacceptable in a physical theory because they would lead to negative-norm states. Consider the$i$-th superpartner of a bosonic particle state,$|i\rangle$, where$i=1,2,\dots,N$. The inner product$\langle i|j\rangle$of such ... 4 There are two aspects. One is sort of trivial and comprehensible; the other is a bit technical. The trivial reason is that$\tilde t \bar{\tilde t}$has two "accents" on top of each other and the symbol therefore occupies too much vertical space which is undesirable because we may get overlapping characters and/or non-uniform spacing between lines. The ... 0$pp$collisions can produce neutralinos and charginos directly via electroweak production. This can occur via$s$-channel$\gamma$,$Z$or$W$, e.g., $$q\bar{q} \to Z \to \chi^0_i \chi^0_j,$$ which is a Yukawa Z-Zino-Higgsino interaction (and is significant if$i\ne j$), or via$t$-channel squarks, which is a$q$-$\tilde{q}\$-Zino interaction. You might be ...

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