A postulated symmetry between bosonic and fermionic fields in quantum field theories and string theories.

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26
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5k views

What if the LHC doesn't see SUSY?

A question in four parts. What are the main problems which supersymmetry purports to solve? What would constitute lack of evidence for SUSY at the proposed LHC energy scales (e.g. certain predicted ...
21
votes
3answers
18k views

What is the current status of string theory (2013)?

I've seen a bunch of articles talking about how new findings from the LHC seem to disprove (super)string theory and/or supersymmetry, or at least force physicists to reformulate them and change ...
2
votes
2answers
367 views

Supersymmetry in Quantum Field Theory

I have an idea of supersymmetry in quantum mechanics, can you suggest a book on "supersymmetry in quantum field theory", which has sufficient mathematical rigour like "Peskin and Schroeder"
2
votes
3answers
477 views

Mathematically: What is SUSY?

Wikipedia says: In particle physics, supersymmetry (often abbreviated SUSY) is a symmetry that relates elementary particles of one spin to other particles that differ by half a unit of spin and ...
7
votes
1answer
139 views

Does anybody know of any good sources that explain (generically) how we form Lagrangians/Actions/Superpotentials for different field content?

I regularly find that I'll understand where the field content in a particular physics paper comes from, but then a Lagrangian or action or superpotential is stated and I don't know how it's derived. ...
10
votes
4answers
600 views

On-shell symmetry from a path integral point of view

Normally supersymmetric quantum field theories have Lagrangians which are supersymmetric only on-shell, i.e. with the field equations imposed. In many cases this can be solved by introducing auxilary ...
8
votes
3answers
346 views

Supersymmetry in Quantum Mechanics

I was reading Supersymmetry in Quantum Mechanics and got stuck in the various mathematical terminology like "Graded-Lie Algebra", "Super Algebra". Is there any good lecture notes concerning these ...
2
votes
1answer
197 views

A certain $\cal{N}=2$ superconformal theory (or is it?)

I want to look at the following theory in $1+1$ dimensions with $\Phi$ being the chiral superfield, $L = \int d^2x d^4\theta \bar{\Phi}\Phi - \int d^2x d^2\theta \frac{\Phi^{k+2}}{k+2} - \int d^2x ...
7
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3answers
685 views

How can string theory work without supersymmetry?

This question is inspired from reading Mitchell Porter's nice answer here to a question asking why supersymmetry should be expected naturally. Among other things, he explains that since weak scale ...
10
votes
1answer
440 views

What does the latest $B_s^0\rightarrow \mu^+\mu^-$ results mean for SUSY?

A paper from the LHCb collaboration just came out last week, stating basically that the $B_s^0\rightarrow\mu^+\mu^-$ decay matches standard model predictions, and people are already shouting that SUSY ...
1
vote
1answer
215 views

Calabi-Yau manifolds and compactification of extra dimensions in M-theory

I just finished learning M(atrix) theory and the basics of the compactification of extra dimensions. The extra 6 dimensions of superstring theory can be compactified on 3 Calabi-Yau manifolds ...
1
vote
2answers
401 views

How exactly do superstrings reduce the number of dimensions in bosonic string theory from 26 to 10 and remove the tachyons?

In bosonic string theory, to obtain the photon as the first excited state, the ground state must have a negative mass (tachyon). By applying $1 + 2 + 3 + \cdots = -1/12$, it can be shown (in a ...
4
votes
1answer
665 views

Dimensional reduction from $3+1$ to $2+1$ for $\cal{N}=2$ vector superfield

Let the supersymmetry transformations for the chiral multiplet $(z_k,\psi_{kL},f_k)$ be, $\delta z_k = 2i \bar{\alpha} \psi_{kL}$ $\delta \psi_{kL} = D_\mu z_k \gamma ^\mu \alpha_R + f_k \alpha_L$ ...
10
votes
1answer
302 views

Auxiliary fields in supersymmetry

I know that auxiliary fields can be used to close the supersymmetry algebra in case the bosonic and fermionic on-shell degrees of freedom do not match. Could somebody please elaborate on this concept ...
15
votes
2answers
388 views

Generalized Complex Geometry and Theoretical Physics

I have been wondering about some of the different uses of Generalized Complex Geometry (GCG) in Physics. Without going into mathematical detail (see Gualtieri's thesis for reference), a Generalized ...
12
votes
2answers
392 views

Alejandro Rivero's correspondence: diquarks and mesons as superpartners of quarks and leptons

The idea of “hadronic supersymmetry” originated in the mid-1960s and derives from the observation that baryons and mesons have similar Regge slopes, as if antiquarks and diquarks are superpartners. ...
8
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4answers
473 views

Using supersymmetry outside high energy/particle physics

Are there applications of supersymmetry in other branches of physics other than high energy/particle physics?
11
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3answers
1k views

What are the mathematical problems in introducing Spin 3/2 fermions?

Can the physics complications of introducing spin 3/2 Rarita-Schwinger matter be put in geometric (or other) terms readily accessible to a mathematician?
9
votes
1answer
240 views

Interpretation of the Instanton in SUSY QM

This is a loose follow up to this question: Interpreting Argyres' spectrum of spontaneously broken SUSY QM. In SUSY QM, the Hamiltonian can be cast as a 2x2 matrix $$ H = \frac{1}{2}p^2 + ...
8
votes
3answers
563 views

What is kappa symmetry?

On page 180 David McMohan explains that to obtain a (spacetime) supersymmetric action for a GS superstring one has to add to the bosonic part $$ S_B = -\frac{1}{2\pi}\int d^2 \sigma ...
7
votes
1answer
319 views

Canonical quantization in supersymmetric quantum mechanics

Suppose you have a theory of maps $\phi: {\cal T} \to M$ with $M$ some Riemannian manifold, Lagrangian $$L~=~ \frac12 g_{ij}\dot\phi^i\dot\phi^j + \frac{i}{2}g_{ij}(\overline{\psi}^i ...
7
votes
2answers
970 views

Can someone give a simple expose on Coleman Mandula theorem and what Mandelstam variables are?

Can someone give a simple expose on Coleman Mandula theorem and what Mandelstam variables are? Coleman-Mandula is often cited as being the key theorem that leads us to consider Supersymmetry for ...
6
votes
1answer
658 views

Definition and difference between the R-symmetry and the $U(1)_R$ internal symmetry

For a general ${\cal N}$ the R-symmetry group is $U({\cal N})$ but for the ${\cal N}=2$ case why is it $SU(2)$ ? I guess it is again different for ${\cal N}=4$. How does one understand this? One ...
5
votes
1answer
170 views

Interpreting Argyres' spectrum of spontaneously broken SUSY QM

I can't understand the spectrum in the figure on page 19 from Argyres' lecture notes on supersymmetry: http://www.physics.uc.edu/~argyres/661/susy1996.pdf Argyres is considering a supersymmetric ...
9
votes
1answer
316 views

Does the ruling out of TeV scale SUSY breaking disfavor grand unification?

One of the arguments in favor of TeV scale SUSY breaking is that it leads to the appropriate running of the gauge coupling strengths leading to grand unification, i.e. $k_Y = \frac{5}{3}$ instead of ...
7
votes
1answer
232 views

Supersymmetry calculations using computer algebra

Already the early papers on supergravity were written using computer algebra software to do some calculations. What modern packages do people normally use for doing such calculations? Of course ...
7
votes
1answer
236 views

Reference for the ${\cal N}=3$ Chern-Simons Lagrangian at general $N_c$, $N_f$

I was wondering if someone could give me a reference where someone has explicitly written the Lagrangian for ${\cal N}=3$ $SU(N_c)$ Chern-Simons theory coupled to $N_f$ fundamental hypermultiplets. ...
6
votes
2answers
189 views

What happens if the holonomy group lies in $SU(2)$ for a CY 3-fold?

I am a mathematician and reading a physics paper about the holonomy group of Calabi-Yau 3-folds. In that paper, a Calabi-Yau 3-fold $X$ is defined as a compact 3-dimensional complex manifold with ...
6
votes
2answers
358 views

Can auxiliary fields be thought of as Lagrange multipliers?

In the BRST formalism of gauge theories, the Lautrup-Nakanishi field $B^a(x)$ appears as an auxiliary variable $$\mathcal{L}_\text{BRST}=-\frac{1}{4}F_{\mu\nu}^a F^{a\,\mu\nu}+\frac{1}{2}\xi B^a B^a + ...
5
votes
0answers
203 views

The ${\cal N} = 3$ Chern-Simons matter lagrangian

This question is sort of a continuation of this previous question of mine. I would like to know of some further details about the Lagrangian discussed in this paper in equation 2.8 (page 7) and in ...
4
votes
2answers
549 views

Superconformal algebra

I had earlier also asked a question about super conformal theories and I am continuing with that, now with more specific examples. I am quite puzzled with it given that I see no book explaining even ...
3
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0answers
165 views

Some more questions on conformal spinors of $SO(n,2)$

This is somewhat of a continuation of my previous question. I had stated there that a conformal spinor ($V$) of $SO(n,2)$ can be created by taking a direct sum of two $SO(n-1,1)$ spinors $Q$ and $S$ ...
2
votes
1answer
447 views

Wilson loops and gauge invariant operators (Part 1)

I guess the Hilbert space of the theory is precisely the space of all gauge invariant operators (mod equations of motion..as pointed out in the answers) Is it possible that in a gauge theory the ...
5
votes
1answer
268 views

T-Duality between Type HE String theory and Type HO string theory

My question is regarding T-Duality between the 2 Type H string theories. I know that the Type II String theories are T-dual to each other because T-Duality changes the sign of the Gamma Matrix so ...
5
votes
1answer
744 views

Relationship between hierarchy problem and higgs fine tuning?

I often hear of hierarchy problem being used synonymous with Higgs fine tuning (esp with regards with motivations for SUSY). What exactly is the relationship between the two problems? As I understand ...
4
votes
1answer
189 views

Argument for quantum theoretic conformality of $\cal{N}=2$ super-Chern-Simon's theory in $2+1$ dimensions

I am using the standard symbols of $V_\mu$ for the gauge field, $\lambda$ for its fermionic superpartner and $F$ and $D$ be scalar fields which make the whole thing a $\cal{N}=2$ vector/gauge ...
3
votes
1answer
145 views

Mass spectrum of Type I string theory

I understand that the massless fields of the Type I string theory are the described by: [\begin{array}{*{20}{c}} {{\rm{Sector}}}&{{\rm{Massless fields}}}\\ {{\rm{R - R}}}&{{C_0}}\\ {{\rm{NS - ...
3
votes
1answer
253 views

Why should SUSY be expected naturally?

In the last 40 years (approximately) people have been "discovering", "rediscovering" and "studying" SUSY as a powerful tool and "symmetry principle". Question: What if SUSY is not realized in ...
3
votes
1answer
207 views

Lorentz spinors of $SO(n,1)$ and conformal spinors of $SO(n,2)$

It would be great if someone can give me a reference (short enough!) which explains the (spinor) representation theory of the groups $SO(n,1)$ and $SO(n,2)$. I have searched through a few standard ...
3
votes
1answer
325 views

The superconformal algebra

How does one derive the superconformal algebra? Especialy how to argue the existence of the operator $S$ which doesn't exist either in either the supersymmetric algebra or the conformal algebra? ...
2
votes
1answer
161 views

Why do the mismatched 16 dimensions have to be compactified on an even lattice?

The mismatched 16 dimensions between the left- (26 dimensional) and right- (10 dimensional) are compactified on even, unimodular lattices. I think I get the unimoduar part, at least intuitively, ...
1
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0answers
90 views

Some questions about flavour and R-symmetry in $2+1$ ${\cal N}=3$ theory

I have heard this fact that for ${\cal N}=3$ theories in $2+1$ with $N_f$ ${\cal N}=3$ matter fields the flavour symmetry group is $USp(N_f)$, $U(N_f)$ or $SO(2N_f)$ depending on whether the gauge ...
10
votes
1answer
71 views

N=2 SSM without a Higgs

In arXiv:1012.5099, section III, the authors describe a supersymmetric extension to the standard model in which there is no Higgs sector at all, in the conventional sense. The up-type Higgs is a ...
7
votes
1answer
362 views

Mathematical concept of supersymmetry

I wish to study supersymmetry in field theory(sometime in december). However, I am quite not sure what is needed for its study. In supersymmetry, I just want to get the mathematical idea, such as its ...
5
votes
1answer
3k views

How would the discovery of Higgs Boson affect superstring theories?

As we probably all know, a new particle similar to Higgs Boson has been discovered. If this turns out to be true, standard model will get a boost (as the discovered mass almost equals to the ...
3
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1answer
91 views

Differential Realizations of certain algebras

I'm a first year graduate student in Mathematical Physics, and I am trying to generalise a certain method involving the so-called "Differential realizations" of certain algebras. The problem I'm ...
3
votes
3answers
232 views

Assuming SUSY is found to be incorrect, what would then be the most compelling candidates for dark matter?

From what I've read, the only remaining candidates appear to be either sterile neutrinos or MOND (MOdified Newtonian Dynamics -- it does seem to keep changing.) Did I miss anything else plausible?
3
votes
2answers
554 views

Missing transverse energy, exact definition

This might seem basic, but it is a bit confusing. You hear about missing transverse energy a lot in SUSY searches due to the LSP which cannot be detected. Let's say I have the 4-vector for the LSP. ...
3
votes
1answer
119 views

Sources for new experimental limits on susy models?

I know the LHC people are publishing new limits every now and then, but as a non-expert in reading experimental papers (yet), I was wondering if there's a friendly website that collects and presents ...
2
votes
0answers
118 views

Supersymmetric Sigma Model

I was working through the Mirror Symmetry book by Clay Math Institute. It deals with supersymmetric sigma model in 10.4 section. It doesn't derive how the action is invariant under the variation. I am ...