Automatical Generator of Conformal Bootstrap Equation

For more information, see autoboot: A generator of bootstrap equations with global symmetry, or An Automated Generation of Bootstrap Equations for Numerical Study of Critical Phenomena.

Some usages also can be checked by typing ?someSymbolName (for example, ?getGroup) in Mathematica. ?somePackageName`* (for example, ?ClebschGordan`*) will give package-lebel information. These usages are also documented in inv.md, group.md.

• Setup
• Usage
• Example

tar xvf sgd.tar.xz

To use autoboot, you have to load either group.m or ngroup.m (not both). ngroup.m requires just one call of setPrecision, which controls the precision of calculation in autoboot.

If you load group.m, all numerical values are rigorous and it takes much time in calculation (in some cases, Mathematica will freeze).

If you load ngroup.m, all numerical values (except for signs, multiplicities and so on) are approximated and it takes much less time.

autoboot supports many finite groups, some Lie groups and product groups of them. More formally, groups which we can treat as a global symmetry of CFT are defined by:

$group = $finite_group | $lie_group | pGroup[$group,$group]
$finite_group = group[$n,$n] | dih[$n] | dic[$n]
$lie_group = su[2] | so[2] | so[3] | o[2] | o[3] | su[4]
$n = positive_integer

Once you get a group G:

1. Set G as a global symmetry by setGroup[G] (if you call this more than once, all values calculated by autoboot previously will be cleared).

2. Register fundamental operators by setOps[...]. 'Fundamental' means that the operator in summation of all primary operator will be treated independently.

3. Get bootstrap equations by bootAll[]. If you need human-readable format, use format[...].

4. (Optionally) You can get a Python code for cboot by toCboot[makeSDP[eq]].

Please see IrrepLabels.md.

Please see CustomGroup.md.

This example generates a bootstrap equation of D8-symmetric CFT. More example codes can be found in sample folder.

(* change the path of autoboot properly *)
SetDirectory["~/autoboot/"];
<< "group.m"
(* getGroup[8, 3] is isomorphic to getDihedral[4] *)
d8 = getGroup[8, 3];
setGroup[d8];
(* set e and v as fundamental operators. rep[5] is the unique 2-dim irrep of d8 (you can check this by d8[ct]). *)
setOps[{op[e, d8[id], 1, 1], op[v, rep[5], 1, 1]}]
format[eq = bootAll[]]
ans = makeSDP[eq];
WriteString["d8.py", toCboot[ans]]
(* specify how to convert operators to latex code *)
opToTeX[e] := "\\epsilon"
opToTeX[v] := "v"
(* specify how to convert irreps to latex code *)
repToTeX[rep[n_]] := TemplateApply["\\mathbf{`n`}", <|"n" -> n|>]
(* you can paste printed string to your latex file *)
Print[toTeX[eq]]