Landscape

Select a theory SU(2): 4 fund + 4 anti-fund (not completed) SU(2): 1 Adj + 1 fund + 1 anti-fund SU(2): 1 Adj + 2 fund + 2 anti-fund (not completed) SU(2): 1 Adj + 3 fund + 3 anti-fund (not completed) SU(2): 2 Adj SU(2): 2 Adj + 1 fund + 1 anti-fund SU(3): 1 Adj + 1 fund + 1 anti-fund SU(3): 1 Adj + 2 fund + 2 anti-fund (not completed) SU(5): 2 rank-2 symm + (conj.) SU(5): 1 rank-2 symm + 1 rank-2 anti-symm + (conj.) SU(5): 1 rank-2 symm + 1 rank-2 anti-symm + 1 fund + (conj.) (not completed) SU(5): 1 rank-2 symm + 1 rank-2 anti-symm + 2 conj. of rank-2 anti-symm + 8 anti-fund (not completed) SU(5): 1 rank-2 symm + 1 rank-2 anti-symm + 2 conj. of rank-2 anti-symm + 1 fund + 9 anti-fund (not completed) SU(5): 1 Adj + 1 rank-2 symm + 1 conj. of rank-2 symm SU(5): 1 Adj + 1 rank-2 symm + 1 conj. of rank-2 symm + 1 fund + 1 anti-fund SU(5): 1 Adj + 1 rank-2 symm + 1 conj. of rank-2 anti-symm + 8 anti-fund (not completed) SU(5): 1 Adj + 1 rank-2 anti-symm + 1 conj. of rank-2 anti-symm SU(5): 1 Adj + 1 rank-2 anti-symm + 1 conj. of rank-2 anti-symm + 1 fund + 1 anti-fund (not completed) SU(5): 1 rank-2 symm + 2 rank-2 anti-symm + (conj.) (not completed) SU(5): 1 rank-2 symm + 2 rank-2 anti-symm + 1 fund + (conj.) (not completed) SU(5): 3 rank-2 anti-symm + (conj.) (not completed) SU(5): 3 rank-2 anti-symm + 1 fund + (conj.) (not completed) SU(5): 2 Adj + 1 anti-symm + 1 conj. of rank-2 anti-symm (not completed) SU(5): 2 Adj + 1 anti-symm + 1 conj. of rank-2 anti-symm + 1 fund + 1 anti-fund (not completed) SU(6): 2 rank-2 symm + (conj.) SU(6): 2 rank-2 symm + 1 fund + (conj.) SU(6): 1 rank-2 symm + 1 rank-2 anti-symm + (conj.) SU(6): 1 rank-2 symm + 1 rank-2 anti-symm + 2 conj. of rank-2 anti-symm + 1 fund + 9 anti-fund (not completed) SU(6): 1 Adj + 1 rank-2 symm + 1 conj. of rank-2 symm SU(6): 1 Adj + 1 rank-2 symm + 1 conj. of rank-2 anti-symm + 1 fund + 9 anti-fund (not completed) SU(7): 1 rank-2 symm + 2 conj. of rank-2 symm + 1 anti-symm + 8 fund (not completed) SU(7): 2 rank-2 symm + 1 fund + (conj.) (not completed) SU(8): 1 rank-2 symm + 2 conj. of rank-2 symm + 1 anti-symm + 9 fund + 1 anti-fund (not completed) SU(9): 2 rank-2 symm + 2 conj. of rank-2 anti-symm + 16 anti-fund (not completed) SU(9): 2 rank-2 symm + (conj.) (not completed) SU(9): 2 rank-2 symm + 1 fund (conj.) (not completed) SU(10): 2 rank-2 symm + 2 conj. of rank-2 anti-symm + 1 fund + 17 anti-fund (not completed) SO(5): 5 vector (not completed) SO(5): 1 Adj + 1 vector SO(5): 1 Adj + 2 vector SO(5): 1 rank-2 symm SO(5): 1 rank-2 symm + 1 vector SO(5): 1 rank-2 symm + 2 vector Sp(2): 1 Adj + 2 fund Sp(2): 1 14 + 2 fund Sp(2): 2 Adj Sp(2): 1 Adj + 2 rank-2 anti-symm + 8 fund (not completed) G2: 1 Adj + 1 fund E[USp(6)] (not completed) All theories Data used in arXiv:2408.02953

$a$ =

$c$ =

$\leq a \leq$

$\leq c \leq$

id =

Search for theories with rational R-charges and central charges.

Chosen Fixed Point

Here is the data for the chosen fixed point.
$F_{UV}$ represents the flavor symmetries in the UV Lagrangian, and $F_{IR}$ represents the flavor symmetries in the IR. $F_{UV}$ and $F_{IR}$ can differ due to accidental symmetry enhancement.
The number of marginal operators, $n_{marginal}$, minus the dimension of flavor symmetries in IR, $|F_{IR}|$, corresponds to the coefficient of $t^6$ in the superconformal index.

#	Theory	Superpotential	Central charge $a$	Central charge $c$	Ratio $a/c$	Matter field: $R$-charge	U(1) part of $F_{UV}$	Rank of $F_{UV}$	Rational
57465	SU2adj1nf2	${}M_{1}q_{1}q_{2}$ + ${ }M_{2}q_{1}\tilde{q}_{1}$ + ${ }M_{3}\tilde{q}_{1}\tilde{q}_{2}$ + ${ }M_{4}q_{2}\tilde{q}_{2}$ + ${ }M_{1}\phi_{1}^{2}$ + ${ }M_{3}M_{4}$ + ${ }M_{4}M_{5}$ + ${ }M_{3}q_{1}\tilde{q}_{2}$ + ${ }M_{6}q_{1}\tilde{q}_{2}$ + ${ }M_{7}\phi_{1}q_{2}^{2}$	0.7286	0.9161	0.7953	[M:[1.0246, 0.8769, 0.9262, 1.0738, 0.9262, 0.9262, 0.6846], q:[0.5615, 0.4139], qb:[0.5615, 0.5123], phi:[0.4877]]	[M:[[2], [-10], [-6], [6], [-6], [-6], [15]], q:[[5], [-7]], qb:[[5], [1]], phi:[[-1]]]	1

Relevant Operators	Marginal Operators	$n_{marginal}$$-$$|F_{IR}|$	Superconformal Index	Refined index
${}M_{7}$, ${ }M_{2}$, ${ }M_{3}$, ${ }M_{5}$, ${ }M_{6}$, ${ }\phi_{1}^{2}$, ${ }q_{2}\tilde{q}_{1}$, ${ }M_{1}$, ${ }M_{7}^{2}$, ${ }\phi_{1}q_{2}\tilde{q}_{2}$, ${ }\phi_{1}q_{1}q_{2}$, ${ }\phi_{1}q_{2}\tilde{q}_{1}$, ${ }\phi_{1}\tilde{q}_{2}^{2}$, ${ }M_{2}M_{7}$, ${ }\phi_{1}q_{1}\tilde{q}_{2}$, ${ }\phi_{1}\tilde{q}_{1}\tilde{q}_{2}$, ${ }M_{3}M_{7}$, ${ }M_{5}M_{7}$, ${ }M_{6}M_{7}$, ${ }\phi_{1}q_{1}^{2}$, ${ }\phi_{1}q_{1}\tilde{q}_{1}$, ${ }\phi_{1}\tilde{q}_{1}^{2}$, ${ }M_{7}\phi_{1}^{2}$, ${ }M_{7}q_{2}\tilde{q}_{1}$, ${ }M_{1}M_{7}$, ${ }M_{2}^{2}$, ${ }M_{2}M_{3}$, ${ }M_{2}M_{5}$, ${ }M_{2}M_{6}$, ${ }M_{3}^{2}$, ${ }M_{3}M_{5}$, ${ }M_{5}^{2}$, ${ }M_{3}M_{6}$, ${ }M_{5}M_{6}$, ${ }M_{6}^{2}$, ${ }M_{2}\phi_{1}^{2}$, ${ }M_{2}q_{2}\tilde{q}_{1}$, ${ }M_{1}M_{2}$, ${ }M_{3}\phi_{1}^{2}$, ${ }M_{5}\phi_{1}^{2}$, ${ }M_{6}\phi_{1}^{2}$, ${ }M_{5}q_{2}\tilde{q}_{1}$, ${ }M_{6}q_{2}\tilde{q}_{1}$, ${ }M_{1}M_{3}$, ${ }M_{1}M_{5}$, ${ }M_{1}M_{6}$, ${ }\phi_{1}^{4}$, ${ }\phi_{1}^{2}q_{2}\tilde{q}_{1}$, ${ }q_{2}^{2}\tilde{q}_{1}^{2}$	${}$	-4	t^2.054 + t^2.631 + 3*t^2.778 + 2*t^2.926 + t^3.074 + t^4.108 + t^4.242 + 2*t^4.389 + t^4.537 + 3*t^4.685 + 6*t^4.832 + 2*t^4.98 + t^5.128 + t^5.262 + 3*t^5.409 + 6*t^5.557 + 6*t^5.705 + 4*t^5.852 - 4*t^6. - 2*t^6.148 + t^6.161 + t^6.591 + 3*t^6.738 + t^6.872 + 6*t^6.886 + 2*t^7.02 + 2*t^7.034 + 6*t^7.168 + t^7.181 + 7*t^7.315 + 7*t^7.463 + 12*t^7.611 + 9*t^7.758 + t^7.892 + t^7.906 + 3*t^8.04 - 6*t^8.054 + 6*t^8.188 - 2*t^8.201 + t^8.215 + 10*t^8.335 + 9*t^8.483 + 4*t^8.631 + t^8.644 - 9*t^8.778 + 3*t^8.792 - 12*t^8.926 + 6*t^8.94 - t^4.463/y - t^6.517/y - t^7.094/y - (2*t^7.242)/y + (3*t^7.685)/y + (4*t^7.832)/y + (2*t^7.98)/y + t^8.128/y + (4*t^8.409)/y + (5*t^8.557)/y - t^8.571/y + (7*t^8.705)/y + (4*t^8.852)/y - t^4.463*y - t^6.517*y - t^7.094*y - 2*t^7.242*y + 3*t^7.685*y + 4*t^7.832*y + 2*t^7.98*y + t^8.128*y + 4*t^8.409*y + 5*t^8.557*y - t^8.571*y + 7*t^8.705*y + 4*t^8.852*y	g1^15*t^2.054 + t^2.631/g1^10 + (3*t^2.778)/g1^6 + (2*t^2.926)/g1^2 + g1^2*t^3.074 + g1^30*t^4.108 + t^4.242/g1^7 + (2*t^4.389)/g1^3 + g1*t^4.537 + 3*g1^5*t^4.685 + 6*g1^9*t^4.832 + 2*g1^13*t^4.98 + g1^17*t^5.128 + t^5.262/g1^20 + (3*t^5.409)/g1^16 + (6*t^5.557)/g1^12 + (6*t^5.705)/g1^8 + (4*t^5.852)/g1^4 - 4*t^6. - 2*g1^4*t^6.148 + g1^45*t^6.161 + g1^16*t^6.591 + 3*g1^20*t^6.738 + t^6.872/g1^17 + 6*g1^24*t^6.886 + (2*t^7.02)/g1^13 + 2*g1^28*t^7.034 + (6*t^7.168)/g1^9 + g1^32*t^7.181 + (7*t^7.315)/g1^5 + (7*t^7.463)/g1 + 12*g1^3*t^7.611 + 9*g1^7*t^7.758 + t^7.892/g1^30 + g1^11*t^7.906 + (3*t^8.04)/g1^26 - 6*g1^15*t^8.054 + (6*t^8.188)/g1^22 - 2*g1^19*t^8.201 + g1^60*t^8.215 + (10*t^8.335)/g1^18 + (9*t^8.483)/g1^14 + (4*t^8.631)/g1^10 + g1^31*t^8.644 - (9*t^8.778)/g1^6 + 3*g1^35*t^8.792 - (12*t^8.926)/g1^2 + 6*g1^39*t^8.94 - t^4.463/(g1*y) - (g1^14*t^6.517)/y - t^7.094/(g1^11*y) - (2*t^7.242)/(g1^7*y) + (3*g1^5*t^7.685)/y + (4*g1^9*t^7.832)/y + (2*g1^13*t^7.98)/y + (g1^17*t^8.128)/y + (4*t^8.409)/(g1^16*y) + (5*t^8.557)/(g1^12*y) - (g1^29*t^8.571)/y + (7*t^8.705)/(g1^8*y) + (4*t^8.852)/(g1^4*y) - (t^4.463*y)/g1 - g1^14*t^6.517*y - (t^7.094*y)/g1^11 - (2*t^7.242*y)/g1^7 + 3*g1^5*t^7.685*y + 4*g1^9*t^7.832*y + 2*g1^13*t^7.98*y + g1^17*t^8.128*y + (4*t^8.409*y)/g1^16 + (5*t^8.557*y)/g1^12 - g1^29*t^8.571*y + (7*t^8.705*y)/g1^8 + (4*t^8.852*y)/g1^4

Deformation

Here is the data for the deformed fixed points from the chosen fixed point.

#	Superpotential	Central Charge $a$	Central Charge $c$	Ratio $a/c$	$R$-charges	Superconformal Index	More Info.	Rational
58939	${}M_{1}q_{1}q_{2}$ + ${ }M_{2}q_{1}\tilde{q}_{1}$ + ${ }M_{3}\tilde{q}_{1}\tilde{q}_{2}$ + ${ }M_{4}q_{2}\tilde{q}_{2}$ + ${ }M_{1}\phi_{1}^{2}$ + ${ }M_{3}M_{4}$ + ${ }M_{4}M_{5}$ + ${ }M_{3}q_{1}\tilde{q}_{2}$ + ${ }M_{6}q_{1}\tilde{q}_{2}$ + ${ }M_{7}\phi_{1}q_{2}^{2}$ + ${ }M_{1}M_{7}$	0.6836	0.8711	0.7848	[M:[1.0588, 0.7059, 0.8235, 1.1765, 0.8235, 0.8235, 0.9412], q:[0.6471, 0.2941], qb:[0.6471, 0.5294], phi:[0.4706]]	t^2.118 + 3*t^2.471 + 3*t^2.824 + t^3.176 + t^3.882 + 3*t^4.235 + 4*t^4.588 + 9*t^4.941 + 12*t^5.294 + 7*t^5.647 - 2*t^6. - t^4.412/y - t^4.412*y	detail	{a: 53739/78608, c: 34239/39304, M1: 18/17, M2: 12/17, M3: 14/17, M4: 20/17, M5: 14/17, M6: 14/17, M7: 16/17, q1: 11/17, q2: 5/17, qb1: 11/17, qb2: 9/17, phi1: 8/17}

Equivalent Fixed Points from Other Seed Theories

Here is a list of equivalent fixed points from other gauge theories.

#	Theory	Superpotential	Central Charge $a$	Central Charge $c$	Ratio $a/c$	$R$-charges	Superconformal Index	More Info.	Rational

Equivalent Fixed Points from the Same Seed Theory

Below is a list of equivalent fixed points from the same seed theories.

id	Theory	Superpotential	Central Charge $a$	Central Charge $c$	Ratio $a/c$	$R$-charges	More Info.	Rational

Previous Theory

The previous fixed point before deforming to get the chosen fixed point.

#	Theory	Superpotential	Central Charge $a$	Central Charge $c$	Ratio $a/c$	$R$-charges	Superconformal Index	More Info.	Rational
55633	SU2adj1nf2	${}M_{1}q_{1}q_{2}$ + ${ }M_{2}q_{1}\tilde{q}_{1}$ + ${ }M_{3}\tilde{q}_{1}\tilde{q}_{2}$ + ${ }M_{4}q_{2}\tilde{q}_{2}$ + ${ }M_{1}\phi_{1}^{2}$ + ${ }M_{3}M_{4}$ + ${ }M_{4}M_{5}$ + ${ }M_{3}q_{1}\tilde{q}_{2}$ + ${ }M_{6}q_{1}\tilde{q}_{2}$	0.7079	0.8764	0.8078	[M:[1.026, 0.8698, 0.9219, 1.0781, 0.9219, 0.9219], q:[0.5651, 0.4088], qb:[0.5651, 0.513], phi:[0.487]]	t^2.609 + 3*t^2.766 + 2*t^2.922 + t^3.078 + t^3.914 + t^4.227 + 2*t^4.383 + t^4.539 + 2*t^4.695 + 3*t^4.852 + t^5.219 + 3*t^5.375 + 6*t^5.531 + 6*t^5.687 + 4*t^5.844 - 4*t^6. - t^4.461/y - t^4.461*y	detail